Is thrice as efficient as B and together they are able to complete a work in 18 days in how many days can a do the work alone?

98.

A and B can complete a work in 3 days. They start together but, after 2 days, B left the work. If the work is completed after 2 more days, B alone could do the work in

4 days
6 days
8 days
10 days

6 days

Work done by A and B in 2 days =

∴ Remaining work

As, B completes the

remaining work in 2 days.
∴ B alone can do it in 3 x 2 = 6 days.

Try to solve the following time and work questions using time and work formula:

Q.1.Ram is twice as efficient as Sunita and can finish a piece of work in 25 days less than Sunita. Sunita can finish this work in how many days?

a) 45 Days

b) 30 Days

c) 90 Days

d) 25 Days

e) 50 Days

Sol : Option E
Explanation:Work Formula: Efficiency of Ramesh: Efficiency of Sunita = 2: 1. Ram will take 1/2 of time as compared to Sunita. Say, Sunita takes 2x days and Ram takes x days. ∴ 2x – x = 25 ⇒ x = 25.

∴Sunita takes 25 × 2 = 50 days to do the work.

Q.2. A can do a piece of work in 16 days, and B can do the same work in 12 days. With the help of C, they finished the work in 6 days. C can do the work in how many days, working alone?

a) 48 Days

b) 24 Days

c) 30 Days

d) 32 Days

e) 40 Days

Sol : Option A
Explanation:C alone will take 1/6 – 1/12 – 1/16 = 1/48 = 48 days to complete the work

Q.3. Chetan is thrice as efficient as Mamta and together they can finish a piece of work in 60 days. Mamta will take how many days to finish this work alone?

a) 80 Days

b) 160 Days

c) 240 Days

d) 320 Days

e) 400 Days

Sol : Option C
Explanation:Chetan is thrice as efficient as Mamta. Let, Mamta takes 3x days and Chetan takes x days to complete the work. ∴ 1/x + 1/3x = 1/60 ⇒ x = 80. ∴ Mamta will take 80 × 3 = 240 days to complete the work.

Q.4.Mr. Ram has a sum of money, which is sufficient to pay Usha's wages for 30 days and Manika's wages for 60 days. If he employs them together, the money is sufficient to pay their wages for how many days?

a) 12 Days

b) 10 Days

c) 30 Days

d) 20 Days

e) 36 Days

Sol : Option D
Explanation:The concept is the same here as the normal time and work problems. Usha’s one day’s wage bill is 1/30 of the total money. Manika’s wage bill is 1/60 of the total money. That means together their wage bill is 1/30 + 1/60 = 3/60 = 1/20 of the total money. Thus, the money is sufficient for their 20 days’ wages.

Q.5.X can do a piece of work in 20 days. He worked at it for 5 days and then Y finished it in 15 days. In how many days can X and Y together finish the work?

a) 10 Days

b) 15 Days

c) 18 Days

d) 24 Days

e) 32 Days

Sol : Option A
Explanation: X’s five day work = 5/20 = 1/4. Remaining work = 1 – 1/4 = 3/4.
This work was done by Y in 15 days. Y does 3/4th of the work in 15 days, he will finish the work in 15 × 4/3 = 20 days. \ X & Y together would take 1/20 + 1/20 = 2/20 = 1/10 i.e. 10 days to complete the work.

Q.6.X can do a piece of work in 30 days. Y can do it in 20 days, and Z can do it in 24 days. In how many days will they all do it together?

a) 6 Days

b) 5 Days

c) 4 Days

d) 4 2/3 Days

e) 8 Days

Sol : Option E
Explanation:They all will take 1/30 + 1/20 + 1/24 = 1/8. ⇒ 8 days to complete the work

Q7.M and N can do a piece of work in 8 days and O can do it in 24 days. In how many days will M, N, and O do it together?

a) 6 Days

b) 5 Days

c) 4 Days

d) 4 2/3 Days

e) 3 Days

Sol : Option A
Explanation:They will together take 1/8 + 1/24 = 1/6 ⇒ 6 days to finish the work.

Q8.One man can paint a house in, '10' days and another man can do it in 15 days. If they work together, they can do it in 'd' days, then the value of 'd' is

a) 6 Days

b) 8 Days

c) 12 Days

d) 10 Days

e) 3 Days

Sol : Option A
Explanation:Total time is d when they are working together = 1/10 + 1/15 = 1/6. ⇒ 6 days to complete the work.

Q9.A can do a piece of work in 9 days and B in 18 days. They begin together, but A goes away three days before the work is finished. The work lasts for

a) 6 Days

b) 8 Days

c) 12 Days

d) 10 Days

e) 3 Days

Sol : Option B Let the work lasts for x days.

B works for x days and A works for x – 3 days. ∴ (x-3)/9 + (x/18) = 1 ⇒ x = 8

Q10.It takes 'h' hours to mow a lawn. In one hour what part of the lawn is mowed?

a) h - 1

b) 1 - h

c) 1 / h

d) h / (1 + h)

e) h

Sol : Option C
Explanation:Total time to mow a lawn = h. ∴ In one hour lawn mowed = 1/h.

Discussion :: Time and Work - General Questions (Q.No.4)

A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

[A].	20 days
[B].
[C].	25 days
[D].	30 days

Answer: Option B

Explanation:

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

If difference of time is 60 days, B takes		3	x 60		= 90 days.
2

So, A takes 30 days to do the work.

(A + B)'s 1 day's work =		1	+	1		=	4	=	2
30	90	90	45

A and B together can do the work in	45	= 22	1	days.
2	2

Rajender said: (Jun 16, 2010)
Please tell me how you have calculated differece of time 2 days.

Sundar said: (Jul 5, 2010)

Hi Friends! The statement "A is thrice as good as workman as B" states that, If A complete a work in 1 day, B will take 3 days to complete the same work. Therefore, if A takes 1 day, B takes 3 days, the time difference is 2 days. If the time difference is 2 days, B takes 3 days to complete the work. Similarly if the time difference is 60 days, then B takes (3/2*60) = 90 days. Then A takes 90 - 60 = 30 days to complete the work.

It is very simple man.

Kumar said: (Jul 5, 2010)

Hi Guys, Let me do the same thing with different values. Given statement : "A is thrice as good as workman as B" Time difference : 60 days. If B takes 12 days to complete a work, A will take only 4 days to complete the same work. So, B takes 12 days whereas A takes 4 days only (because A is thrice as good as B). Here time difference is 12 - 4 = 8 days. If the time difference is 8 days, B takes 12 days. Similarly if the time difference is 60 days, then B takes (12/8 * 60) = 90 days.

...Rest thing you can understand from the explanation part.

Bharathi said: (Jul 9, 2010)
Dear Friends, In this question atlast we got (a+b)'s 1 day work=2/45. How it is changed to be an A and B are together can do the work in 45/2.

Nagu said: (Jul 12, 2010)
Hi Bharathi, If A takes 10 days to complete a work means A's one day work is 1/10 so complete this work A takes 10/1 days is same as 10 days Sat the same way (A + B)'s 1 day's work 2/45 means They will take 45/2 = 22 1/2 days I think you got my point have a nice day

SHEETAL said: (Aug 3, 2010)

Hi Guys, Don't be confused in data given in question. I have one short cut to solve such kind of question. A is K times as good a worker as B & takes X days less than B to finish the work. Then the amount of time required by A & B working together is K * X / K'S SQUARE - 1. SO IN QUESTION K IS 3. X IS 60. SO PUTTING THE VALUES IN ABOVE MENTIONED FORMULA. K * X / K'S SQUARE - 1 =3 * 60 / 9 - 1 =3 * 60 / 8 =180 / 8 =22.5 DAYS AS MENTIONED OPTION B. I HOPE U WILL UNDERSTAND THIS THING & WILL APPLY IN QUESTION BASED ON THIS.

All the best. Have nice day!

Sangeetha said: (Aug 4, 2010)
Oh thanks sheetal

Indhu said: (Sep 1, 2010)

Hi friends,. Though content is big it is easy to understand. Work done by A as compared to B=3:1. Time taken by A as compared to B=1:3. So, time difference is 2. A will finish the work 60 days lesser than B. Therefore time difference is 60. Time taken for A = 60/2 = 30. Hence time taken for B=3* time taken by A = 90. If A+B can do a piece of work in n days, then (A+B) 's 1day's work=1/n. Working together (A+B) 's one day work = (1/30) + (1/90) =2/45. If (A+B) 's 1day's work=1/n, then A+B can finish the work in n days.

Therefore total time taken = 45/2= 22. 5 Days.

Prashant said: (Sep 15, 2010)
Suppose B takes x days to finish the work and then according to question A will take (60-x) days to work. in question the ratio of time taken is 1:3 therefore 1/3= (60-x)/x x=45 So A can complete the work in (60-x)=(60-45)=15 days So (A+B) one day's work =(1/15 + 1/45) =4/45 So (A+B) complete the work in 45/4 = 11 1/4 days.

Sugumaran said: (Sep 22, 2010)
Ratio of time taken=1:3 A finish the work in 60 days and B in x days. 1:3::60:x x=180 days So, A and B 1'days work 1/60+1/180=45 days Is it correct or not?

M.Atul said: (Sep 23, 2010)
@Sugumaran please read carrefully problem. Though you have got same answer but it doesn't satisfied second condition that differnce in day should be 60 not 120.

Priya said: (Sep 23, 2010)
Please tell me why we are taking 3/2 to multiply with 60. Please explin me.

Harsha said: (Oct 13, 2010)

A clear approach: Given: A's time taken:B's time taken=1:3 So A's proportion of time taken=1/(1+3)=>1/4*some x B's proportion of time taken=3/(1+3)=>3/4*some x As it is said that difference of time is 60 days B's time-A's time=60 => 3x/4-x/4=60 =>x=120 So A's proportion of time taken =x/4=120/4=30 days B's proportion of time taken =3x/4=3*120/4=90 days A's 1 day's work = 1/30 B's 1 day's work = 1/90 (A + B)'s 1 day's work = (1/30 + 1/90)= 4/90=2/45

A and B together can do the work in 45/2 = 22 1/2 days.

Naveen said: (Oct 26, 2010)
Hi, in prashanth answer, he equals the ratio 1/3 to 60-x/x but it actually x-60/x.

Shilpi said: (Nov 18, 2010)
Can you pls teach me this equation 1/30+1/90=4/90

ASHIRWAD said: (Nov 27, 2010)
HI FRIENDS THIS IS THE simplest method for solving this type of que.... K*S/(A^2-1) where S=DAYS FOR FINISHING WORK(60 GIVEN IN QUE) K=3 GIVEN IN QUE

Ashirwad Dubey said: (Nov 28, 2010)
Hi friends k*x/(k^2-1) k=3 x=60 given in que ok friends

Vikas said: (Dec 29, 2010)
I didnt understand how did we get that (3/2)*60 ?

Showry said: (Jan 5, 2011)
Hi Friends, A:B=1:3 time taken.........since A is 3 good as B A takes 60 days less than B B-60:B=1:3............ i.e B-60/B=1/3..... B=90 days.... A=30...... (A+B)'s one day work (1/30+1/90) = (2/45) Total work by (A+B) is 45/2 i.e 22 1/2.............

Gowri said: (Jan 8, 2011)
kl/(k)^2-1 k=3 l=60 3*60/(3)^2-1 =45/2 =22.5

Nagarjun said: (Jan 13, 2011)
@Vikas Its just cross multiplication. If the difference is 2 days then b takes 3 days If the difference is 60 days then b takes x days Hence, x= (60*3)/2. I think you got it now.

Naresh Kumar said: (Jan 18, 2011)
Thank you guys.

Malini said: (Jan 19, 2011)
Sheetal thanks a lot dear. This short cut is very much easy.

Baskar said: (Jan 21, 2011)
@bharathi i think u r in confusion.. just know dat work = day.. 1 day = 2/45 works.. in ques ask abt "work"? den cross mul 1 work = 45/2 days.. now u got it

G.P. said: (Feb 10, 2011)
SIMPLE AND BEST WAY since a is thrice better than b hence a:b=1:3 similarly a takes 60 days less than b hence a:b=(b-60):b=1;3 cross multiplication n we get 3b-180=b hence b=90days hence a=30days 1/90+1/60=4/90 hence total daysreciprocal 90/4=45/2

Nishant said: (Feb 10, 2011)
@ G.P. Thanks. I like the way you solve it.

Balaji said: (Feb 19, 2011)
Showry you explained superbly.

Prathyusha said: (Feb 28, 2011)
SIMPLE AND NICE EXPLANATION!... @KUMAR

Vani said: (Mar 18, 2011)
Showry's explanation is good.

Siva said: (Apr 21, 2011)

Hi Guys, I think following simple method (alternate) will make you more clear, A can complete work in N days => A's 1day work = (1/N)----1 B can complete work in n days => B's 1day work = (1/n)----2 Given data, A thrice as B so , A=3B A complete work 60 days less than B so, (N=n-60) Apply in 1 & 2 A's 1day work = (1/(n-60))-----3 B's 1day work = (1/n)--------4 we know that A=3B ; B=(1/n) so,Apply B in A we get[A=3/n] Apply in 3 3/n=(1/(n-60)) by solving, 3n-180=n n=90 so, B can complete work in 90 Days => B's 1 Day work =(1/90) we know that N=n-60, so, A can complete work in 30 Days => A's 1 Day work = (1/30) (A+B) 1 Day work = (1/30 + 1/90) by solving we get, A+B 1 Day work = 2/45,

so A and B together can complete work in 45/2 Days.

Hindu said: (Jun 25, 2011)
Hai sheetal your shortcut method helps lot to understand so quickly its really super.

Naveen Kumar said: (Jul 1, 2011)

Hi friends, Here is a simple technique to calculate the above problem.... Given, If the If difference of time is 2 days, B takes 3 days. If difference of time is 60 days, B takes......? We can represent the above relation like this, 2------->3 60------>....? By cross multiplying the above terms we will get... 60*3/2 = 90. Note:- Always individual term should come in the denominator. By applying the above procedure you can solve any problem of this type....

I think this technique will help you while doing with this type of problems...

Abdul said: (Jul 9, 2011)
Hey Siva your way of solving is fantastic and understandable! Thanks.

Jezan said: (Jul 17, 2011)
According to this question if A is x, B will be x+60 1/3=x/x+60 3x=x+60 2x=6 x=30 A+B'S ONE DAY WORK=1/30+1/90=2/45 SO WHOLE WORK S= 45/2( UPSIDE DOWN) 22.5 DAYS. HOPE ALL LL GET DIS

Jaswinder Singh said: (Aug 14, 2011)
Ratio of times taken by A and B = 1 : 3. or 1x:3x so, we say 3x-1x=60, 2x=60, x=30, so A will 30 day to complected a work, B will be complete the work ie 3x, 3(30)=90days, (A+B) 1 Day work = (1/30 + 1/90) by solving we get, A+B 1 Day work = 2/45, so A and B together can complete work in 45/2 Days.

Sharan said: (Aug 21, 2011)
@Jaswinder singh: I understood your explanation man. Thanks.

Sundar said: (Aug 22, 2011)

@All (Must read if you have any doubts) If B takes 3 days then A takes 1 day to complete the task. Time taken Ratio => A : B = 1 day : 3 days. 1 3 (difference is 2) 10 30 (diff 20) 30 90 (diff 60) <= Here diff is 60 days, So this is the correct ratio to be used in calculation, since it was mentioned in the given question. A alone can finish the task in 30 days. B alone can finish the task in 90 days. Work done by A alone in 1 day = 1/30 Work done by B alone in 1 day = 1/90 Work done by A and B in one day (1/30 + 1/90) = 3+1/90 = 4/90 The no. of days required to complete the task by A and B is = 90/4 = 22.5 days. ////**** Important Note: ****//// We cannot take other ratios like 1:3, 10:30, 40:120, 60:180 for the calculation. Since the diff is mentioned as 60 days. Because, it will give different answers for each different ratios used for calculation. If we take 1:3 => (1/1 + 1/3) = 4/3 If we take 10:30 => (1/10 + 1/30) = 4/30 If we take 40:120 = (1/40 + 1/120) = 4/120 If we take 60:180 => (1/60 + 1/180) = 4/180 ... so on.

I hope this will help you. Have a nice day!

Deepti said: (Aug 25, 2011)
It is not so big and easy to understand. let work done by B in 1 day = 1/x so work done by A in 1 day = 1/(x-60) 1/(x-60) = 3/x so x = 3x - 180 x = 90 work done by A and B in 1 day is 30 and 90 respectively work done by both together in 1 day = 1/30 + 1/90 = 2/45. total work done = 45/2

Harsha said: (Sep 1, 2011)
Easy method : A can completed in x days B can in 3x days then A = B-60 (A can do in 60 days less than B ) => x=3x-60 => x= 30 => A=30, B=90 Then together work done is (1/30+1/90) = 2/45. Finally total work done is 45/2.

Pinky said: (Sep 10, 2011)
@Sheetal superb explanation.

Praveen said: (Sep 16, 2011)
Nice exp. Harsha.

Nitin Singla said: (Sep 23, 2011)
Hey its simple to understand. Days taken by B = x Days taken by A= x - 60 Their time taken proportio is 1:3 so, x - 60/ x = 1/3 x=90; So A will do the work in = 30 days abd B in 3x= 3*30=90 days, and u can find their 1 day's work and ad it. Simple :)

Srinivas said: (Sep 25, 2011)
Hi friends, Given A:B=1:3 Therefore B=3A--------equation 1 let B can do a work in x days. then A can do the same work in (x-60) days. then B=3A x=(x-60)3 therefore x=90 days therefore B can do a work in 90 days. and A will do a work in 90-60=30 days.

Pavethra said: (Sep 29, 2011)
I tell that A is thrice as good as B so it should be 3:1 na. Am I right?

Sunil Reddy said: (Oct 4, 2011)
We can use a simple formula here:[(KL)/k squqre-1)] -->here K=3(efficiency),L=60(time) so (360/(33)-1)=>180/8=221/2

Vinod Reddy said: (Nov 7, 2011)
THANK U SHEETAL,your short cut method is simply super.there is no words to say

Sundar said: (Nov 18, 2011)
If difference of time is 60 days 3*60/2 = 90 days. I can't get this step? Please explain.

Riyaz said: (Nov 23, 2011)

Ratio of times taken by A and B = 1 : 3. That is If A takes 1 day B takes 3 days Time Difference is 3-1 = 2 days Here is the tricky part : If A takes 1/2 day B takes 3/2 days Time Difference is 3/2 - 1/2 = 1 days When time difference is 60 days (Just mulitply by 60) A takes 60/2 and B takes 3*60/2 So, A takes 30 days to do the work. and B takes 90 days to do the work. A's 1 day's work = 1/30 B's 1 day's work = 1/90 (A + B)'s 1 day's work = (1/30 + 1/90)= 4/90 = 2/45

A and B together can do the work in 45/2 = 22+1/2

Anu said: (Nov 27, 2011)
Awesome explanation HARSHA

Brajesh Anuragi said: (Nov 28, 2011)
Thanks Showry for given the simple and correct ans.

Gauarv said: (Dec 27, 2011)
Thanks harsha.

Neeraj said: (Jan 8, 2012)
A will finish the work 60 days lesser than B. What is it mean please explain?

Abhay said: (Jan 10, 2012)
@Neeraj-A will finish the work 60 days lesser than B,means if B takes 60 days to complete the work,A takes 1 day.

Sureshkumar said: (Jan 19, 2012)

Another easy way 2 find out: 1st put the ratio i.e.1:3(A:B) 2nd the condition given here is A can work less than 60 days So, find out the probability that matches with the ratio condition(A&B must be difference 60 here) for eg:let we take as A as 20 therefore B must be 60(here we get the difference as 40 only)according to 1:3 which cant satisfy The given condition(A less than B by 60 days) suppose you take A as 30 means you get B as 90 which is greater than 60 days of A....A=30 B=90 A's 1 day work=1/30

B's 1 day work=1/90 A+B's 1 day work =1/30+1/90=4/90 here they are not given to find out as 1day work...so take as 90/4=22.5 <==> 22(1/2).

Varma said: (Jan 26, 2012)
Nice formula @Sheetal.

Aarush said: (Feb 16, 2012)
Thanks sheetal.

Raman(UIET,KUK) said: (Feb 17, 2012)
Guys check this out and don't be confused.... as we know A is 3 time better than B and A takes 60 days less than B so, time taken by A: time taken by B= 1:3 = b-60:b ( suppose time by B is b) by cross multiply, 3b-180=b i.e. b=90 so time taken by B=90 and time taken by the A is=90-60= 30

TABISH said: (Feb 18, 2012)
@sheetal do not able to understand how you get that formula to calculate the time i.e. K*X/K^2-1

Kapil said: (Feb 20, 2012)
Nic Explanation. . .Sheethal. . .

Shro said: (Feb 20, 2012)
Indhu very easy simple explanation as per the question. Good :) thanku :)

Sindhu said: (Feb 23, 2012)
HI, This method I feel to be quiet easier. A is thrice as good as workman as B. therfore, A=3B -(1) finish a job in 60 days less than B 1/B=60+1/A -(2) i.e B`s One day work = A`s one day work + 60 days. Solve (1) & (2) we will get A= 90; From (1) B=A/3 => B= 30. (A+B)`s 1 day work = 1/90+1/30 =2/45 =22 1/2 days

Iyappan said: (Apr 12, 2012)
Naveen kumar your explanation is beautiful for me.

Sanchi said: (Jun 3, 2012)
Very simple way. 3A=1B B takes x days. 3 (x-60) =x 3x-x=180 X dats is B=90, A=30. Now, 1/90+1/30=22. 5.

Nitin Singh Parihar said: (Jul 5, 2012)
Let B do the work in 'x' days. So, A will take (x-60) days. Now, ratio of A:B=1:3 (given in ques). So, 1/3=x-60/x. => x=90 (B's 1 day work). So, A's work=30 days. Working together=1/30+1/90. =45/2 days. Easy and simple.

Akansha said: (Aug 7, 2012)
B takes 3 times more days than A. i.e. B=3A. So. B-A=60. 3A-A=60 =>. A=30. B=90. Now calculate 1 day work of A and B.

Sunny said: (Aug 26, 2012)

A is thrice as good as workman as B means 1:3(Ratio) Therefore A is able to finish a job in 60 days less than B So A= 1/60 and B=1/60 .....(Given) According to the ratio A=1/60 B=1/3*60 (As we are calculating by days) So Now A = 1/60 < B = 1/90 (A finishes work less than B) Working together, they can do it in: 1/A+B = 1/60 + 1/90 (As we are calculating by days)) 1/A+B = 2/45 So A+B = 45/2 Days

Option (B) is the correct ans

Vidya said: (Aug 27, 2012)
Can you please solve this using unitary method. Its b'coz I follow that method.

Anji said: (Sep 4, 2012)
Let the time taken by A be x days, then time taken by B will be 3x days. Given that, time taken by A to finish the work = time taken by B -60 i.e, x=3x-60 => x=30. Therefore, time taken by A to finish the work is 30 days. so B takes 90 days. Now ,work done by A & B in 1 day=1/30 + 1/90 =4/90 =2/45 Time taken by A & B to complete the work=45/2 days =22 1/2 days

SANJEEV said: (Sep 11, 2012)

#include<stdio.h> void main() { float a,b; int c,d; printf("enter ratio of A : B\n"); scanf("%f",&a); printf("enter no of days lesser than B by A to complete work\n"); scanf("%f",&b); c=ab/(a-1); d=c-b; printf("no of days to complete work by A and B is %d",(c*d)/(c+d));

}

Prabha said: (Sep 24, 2012)
If difference of time 2 days B takes 3 days Similarly why don't we take difference of time 60 days B takes 60*3 is 180 days. Please explain to me ?

Joshi Sir said: (Nov 21, 2012)

Friends, don't make it complex: Here we go. Ratio of time taken by A & B = 1:3 And A takes 60 days less then B Suppose, days taken by B = x then days taken by A = (x - 60) Thus, A : B = (x - 60) : x 1 : 3 = (x - 60) : x 1/3 = (x - 60) / x X = 3 (x - 60) X = 3x - 180 180 = 3x - x 180 = 2x X = 180 / 2 = 90 Hence, Days taken by B = x = 90 days Days taken by A = (x - 60) = 90 - 60 = 30 days 1 day work of A and B = 1/30 + 1/90 = 4/90 = 2/45 So,

Total days taken by A & B to complete the work = 45/2 = 22.5 days

Ashutosh said: (Nov 29, 2012)
Formula-->nx- (n+1) /nx. 4x-4x/3=60 so x=45/2.

Keerthi said: (Jan 10, 2013)
So by the explanation above we have to take in the ratio 1:3.

Kavya said: (Jan 10, 2013)
A is twice as good a workmen as B and together they can finish a piece of work in 18days. In how many days will A alone finish the work? Can we solve the above problem using the formula k*x/k^2-1.

Pankaj said: (Feb 5, 2013)
Let A takes x days to do the work alone Therefore days taken by b is (x+60). Now A is 3 times faster than B So no.of days taken by A will be 3 times less than B. So 3*x=(x+60) 2x=60 x=30 days //work done by A Work done by B=30+60=90 days. Now we can find work done together 1/30 +1/90 to get the answer.

Monika said: (Feb 11, 2013)
We have a direct formula for these kind of questions .. i.e., Work done together is given by = (md)/(m^2 - 1), Where d is no of days taken by B and m is no of time A is faster than B, Therefore = (360)/(3^2-1) = 22.5.

Praveen said: (Mar 10, 2013)

@All. Please refer to Sheetal's response as given below. Its the best and easiest way to solve such questions. PS:Thanks sheetal. "A is K times as good a worker as B & takes X days less than B to finish the work. Then the amount of time required by A & B working together is K * X / K'S SQUARE - 1. SO IN QUESTION K IS 3. X IS 60. SO PUTTING THE VALUES IN ABOVE MENTIONED FORMULA. K * X / K'S SQUARE - 1 =3 * 60 / 9 - 1 =3 * 60 / 8 =180 / 8 =22.5 DAYS.

AS MENTIONED OPTION B.

Sridhar said: (Apr 28, 2013)
Simple way: A and B ratio 1:3. Since A finishes 60 days lesser than be A takes 90 days and B takes 30 days. So per day calculation (1/90+1/30) = 22.5 days.

Vinod Anand said: (May 22, 2013)
If A is thrice as good as workman B, Than A=3B ----(1) or B=A/3 --------(2). If A is finish a job in 60 days less than B. Than A = B-60. Put the value of B from Eq.(2). A = A/3 -60 3A = A-180 2A = 180 than A = 90 Days. Same Put the value of A in Eq.(2). B=90/3 = 30 Days. So Working together (A+B) = 1/90 + 1/30. A+B = 2/45. or A+B =45/2 = 22.5 or 22 1/2. Answer.22 1/2 Days.

PARASHAR said: (May 31, 2013)
Simple yaar. >A is thrice as good as workman as B and therefore is able to finish a job in 60 days=IF B TAKE 90 DAYS THEN A WILL TAKE 30 (60 DAYS LESS). >1/30 (PLUS) 1/60=4/90==>90/4==>22. 5 SIMPLE.

Thirupathi Malavath said: (Jul 24, 2013)
Simple method: Say B completes the work in 'x' days. Then A will take (x-60) days to finish the work. Since A is thrice as good as B, 3A=B. Therefore, 3 (x-60) =x, x=90. B's 1 day work=1/90, A's 1 day work=1/30. (A+B) 's 1 day work= (1/90+ 1/30) =2/45. Therefore, both can finish the work in 45/2 days i.e., 22 1/2.

Ankush Rana said: (Aug 9, 2013)
A is twice as good as workman B and together they finish a piece of work in 14 days. A alone can finish the work in.

Sam said: (Aug 10, 2013)
Did they mention that difference of working time is 60 days.

Shivaram Vollala said: (Aug 21, 2013)

In the given question the ration of capacity of work in day a:b is = 3:1. So always inverse proportion to capacity and work like the way a and b can do the work ration =1:3 i.e. a's one day work = b's three days work. So let now finish work together is imagine x. Ratios of each person a's work = x* 1/4 = X/4. (1). Ration of b's work = x* 3/4 = 3X/4. (2). In the given question difference is 60 days. So 3X/4-X/4 = 60 Days. Solove ther x we get x = 120. Now substitute x in (1) and (2). W e get a's part of one day work = 30 days. And b's part of one day work = 90 days. Now solve the. A and B together work = 1/30+1/90 = 4/90 =2/45.

This is and b together part of work now one day work = 45/2 = 22.5 days.

Sudhanshu said: (Sep 19, 2013)
Why so many stories I don't know. Its as simple as this: A's 1 day's work = x. B's 1 days work = x+60. So, total one day's work is. 1/x + 1/x+60 = 1. And you get x = 30 that is total days required for A to cmplete the work where B's value gets 90 days. Rest you can solve.

Malay Kanti Bhunia said: (Sep 21, 2013)
X - 3X = 60. X = 30. A done works 30 days and B done the work 90 days. A work done in 1 day 1/30 part. B work done in 1 day 1/90 part. A and B work together in 1 day (1/30+1/90) = 2/45 part. Time taken in this work 22.5 days.

Jag Parvesh said: (Dec 22, 2013)

Ratio of times taken by A and B to finish a work is 1 : 3. A:B=1:3 OR A/B=1/3 or 3A=1B --(1). B-A = 60. B-(1/3)B = 60 (Substituting the value of A from eq 1). 3B-B = 180 (Multiply through by 3). 2B = 180. B = 180/2. B = 90. A = (1/3)*90. A = 30. So, A can do the job in 30 days. Therefore, A can do 1/30 of the job per day. And B can do the job in 90 days. Therefore, B can do 1/90 of the job per day. Work they can do per day: = (1/30) + (1/90). = (3/90)+(1/90). = (3+1)/90. = 4/90.

So the job will take 90/4 days, which is 45/2 or 22.5 days.

M Ahmad said: (Feb 4, 2014)
A can do the job in x days. B can same job in 3x days. 3x=x+60 by B. x=30. One day work by A and B = 1/30+1/90 = 4/90 = 2/45. Whole job done by A and B = 45/2 = 22.5 days.

Michael said: (Mar 25, 2014)
How do we get 4/90 ?

Mancy said: (Apr 12, 2014)
Hi @Michael, By taking the L.C.M of 30 & 90 you'll get 90. Now, here the value become. =1/30+1/90. =(3+1)/90. =4/90. =2/45. So, 2/45 is total work done by them, But we've to find the days. By formula work to days. N work = 1/N days. So, 2/45 = 45/2 days. Answer = 22.5days.

Sundar said: (Apr 23, 2014)
Please Tell me how 3/2 has come?

Atul1487 said: (Apr 28, 2014)
What is need to take time difference? How will I come to know that I need to calculate time difference?

Venkatesh said: (May 21, 2014)
Hi friends just read, A's works 3 times than B so work ration 3:1 and time ratio will be 1:3 in the question they ask for time so 3/(3-1)*60=90. A 3 times better 3/90=1/30(1 days work) B 1/90 1days work together 1/90+1/30=answer.

Poornachandran said: (May 24, 2014)
Guys, I'll tell by simple method. Given, A is thrice of B. So A = 3B---->(1). A's 1 day work is A=1/60--->(2). Substitute (2) in (1), A=3B. We get, 3B=1/60. B=1/180. In question they asked A+B=how many working days? We know A and B values. Add A and B. 1/60+1/180=1/Work days. Take L.C.M. 3+1/180=1/Work days. 4/180=1/work days. 1/45=1/work days. Work days=45. By fraction we can write 22 1/2 days.

Kumar said: (May 26, 2014)
How its "4/90 " ?

Nithya said: (Jun 24, 2014)
Lets B takes x days to complete the Work, Then B 's Capacity ==>1/x. A is 3 times as good as A so A'S capacity is 3/x. Then Time Taken by B is = x/1. Time taken by A is = x/3. Time difference (x-x/3)=60. Which gives x = 90. Time taken By B = 90. Time taken By A = 30. (A's Work +B's Work) 1 day Work = (1/30)+(1/90). = 4/90. Then Time taken to complete work is 90/4 ==> 22.5 days.

Pranay said: (Jul 13, 2014)

The work being done by A & B is in ratio of 1:3. This means if A does a work in 1 day, than B will do this work in 3 days. Now let suppose this ratio is multiplied by a factor, say x. Then ratio becomes x:3x. Now another relation given is that A can do work 60 days faster then B. Mathematically we can write it as. x=3x-60. Solving this, we get x = 30. Hence the ratio becomes 30:60.

Now we can calculate the time taken by them.

Thaha said: (Jul 22, 2014)

"A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B." Solution: ********* 'A' able to finish a job in 60 days 'less than B'. Let A's work is = x days. Let B's work is = 3x days. A able to do a work in 60 less than B. Therefore, A's work = B's work - 60. So, x=3x-60. Then x=30. A can complete the work in 30 days. B can complete the work in 3*30 = 90 days. A's one day work = 1/30 days. B's one day work = 1/90 days. A+B one day work = (1/30)+(1/90) = 4/90 days. Therefore A and B can finish the work in = 90/4.

So the answer is : Option [B].

Kalyani said: (Jul 28, 2014)
What is the meaning of taking 3/2 in the problem. What's that ratio about?

Piyasa Dey said: (Aug 20, 2014)

If A does a work in 1 day. therefor B does the same work in 3 days since A is thrice as good as workman as B. Let A completes the work in x days, B will take (x + 60) days more than A takes. Therefore 1:3 :: x :(x + 60). Now according to the formula if a:b :: c:d. Then it is considered as (a * d) = (b*c). Applying this formula we get 1*(x + 60) = 3*x. By solving we get x= 30 i.e A takes 30 days to complete the work. Therefore B will take (30+60)=90 days. A's one day work = 1/30 days. B's one day work = 1/90 days. A+B one day work = (1/30)+(1/90) = 4/90 days.

Therefore A and B can finish the work in = 90/4.

Deepak Patgar said: (Aug 22, 2014)

Let A completes work in x days. So no of days taken by B to complete the same work will be 3x days. A takes 60 days less than B. So 3x-60 = x. 2x = 60. x = 30 days (number of days taken by A). 3x = 90 days (number of days taken by B). Work done by A per day is 1/30. Work done by B per day is 1/90. Work done the together in 1 day will be (1/30+1/90) = 4/90. So work done by them in 10 days will be 40/90. Work done in 20 days 80/90. Number of days require to do the remaining 10/90 will be 2.5 days.

Ans = 22.5 days.

Poor Gamer said: (Aug 29, 2014)
Let A takes x days and B takes 60+x days. Its given that A takes 1 days when B takes 3 days. So, 1/3 = x/x+60. Cross multiply and we get x = 30 i.e A. X+60 = 30 + 60 = 90 i.e B. Remaining as usual.

Divyanshu Dwivedi said: (Sep 2, 2014)
Simple: A's work = x. B's work = y = 3x. Hence acc. to ques.: 3x - x = 60 ;. x=30 A's. y=90 B's. Now.... 1/30 + 1/90 = 1/z. z = 90/4 Answer.

Mohit Jain said: (Dec 4, 2014)
Let, A takes = x days. B will take = 3x days. Difference 3x-x = 60. So 2x = 60. x = 30 days. Thus A can do it in 30 days and B in 90 days.

Sumit said: (Dec 8, 2014)
If difference of time is 60 days, B takes 3/2 x 60 = 90 days. Please explain this statement.

Prakash said: (Dec 15, 2014)
But there is not given difference in question they given A finish work in 60 day?

Ankita said: (Jan 12, 2015)
If B takes y days , A takes (y-60 ) days. Now , their efficiency are A:B = 3x : x. So total unit of work is 3x(y- 60 ) man days = xy man days. Calculating this we get y = 90. So if B worked for 90 days, A worked for 30 days. Hence 1/30 + 1/90 = 22 1/2 days :).

Priya said: (Mar 17, 2015)
No need to do all that simply guess numbers 30 & 90 which is satisfying this then without using pen we can get answer 22.5 days.

Ankita said: (Apr 5, 2015)
Suppose A takes x days. Then, B will take 3x days. From question, 3x-x = 60. => x = 30. => A takes 30 days and B takes 90 days. Together they will take = 3090/30+90. = 3090/120. = 90/4. = 22.5 or 22 1/2 days (ans).

AaA said: (Apr 7, 2015)
Is there a fixed formula for this?

Govardhan Reddy said: (Apr 9, 2015)
Why were their difference between days? Please explain to me.

Sachin said: (Apr 28, 2015)
Its very simple. Suppose B's done work = X day. Then A's done work = (X-60) day. Efficiency ratio is. A : B = 1:3. (X-60) : (X) = 1:3. X = 90. So A's take days = 30. B's take day = 90. A's 1 day work = 1/30. B's 1 day work = 1/90. (A+B) s 1day work = 1/30 + 1/90 = 2/45. So together they will take = 45/2.

Raj said: (May 15, 2015)
Easy lets assume A works total days = X. So A one day work = 1/X. B is working 3 times less than A. So Total days of B is = 3X. So B Works one day = 1/3X. Different between total days of B and A is 60. So 3X-X = 60. 2X = 60. X = 30. Now normal maths. Replace X with numbers. You will get answer. So 1/30-1/90 = 22.5.

Arjun said: (May 18, 2015)
Can any one give me a easier way using LCM method?

Mohit Agnihotri said: (May 25, 2015)
Work done ratio (A:B) = 3:1. And let x be no. of days taken by B. So, A:B = x-60:x {Given- A finish a job in 60 days less than B}. Now, (x-60)/x = 1/3. 3x-180 = x => x = 90. It means A takes 30 days and B takes 90days. One day work of A and B is 1/30+1/90 = 4/90. Thus, 90/4 = 22.5 days required to complete the work.

Pratyush said: (Jun 8, 2015)
Can we do it like this: a = 3b....(1). a-b = 60. 3b-b = 60. 2b = 60. b = 30. If b = 30 then from 1a = 3x30 = 90. Now, = 1/30+1/90. = 3+1/90. = 4/90 = 2/45. = 45/2 = 22.5 days.

Neeraj said: (Jun 11, 2015)
Shortcut: A & B together will complete in 6/14/8 = 24/7 days = 3 3/7 days. Work completed in 3 days. So C's share 3/7 days. Now 3200/24/7*3/7 = 400.

Rajat Singh said: (Jun 16, 2015)
Simple solution: a = 3b. a-b = 60 (difference of b). 3b-b = 60. b = 30, a = 90. So they can together work in 1/30+1/90 = 4/90. :->22.50.

Megala said: (Jul 2, 2015)
Please explain last 2 steps.

Surya said: (Jul 11, 2015)
Simple formula with solution: (D) n/n2 (i.e n square)-1 = work together. Details: D-60, n-3, by putting the formula = (60)3/3's square-1 = 22.5 days.

Sharad said: (Jul 15, 2015)
Given A is thrice as good as B, Therefore 3:1. i.e 3x:x (ability to work). (Time taken is inverse of work). Time taken by A and B to complete work = x:3x. Difference A-B = 60. Therefore x-3x = 60. x = 60/2 = 30. Now x:3x = 30:3(30). = 30:90. (A+B) 's 1 day = (1/30)+(1/90). 1 day = 2/45 work. 45/2 day = 1 work. 22. 5 day = 1 work.

Malleswari said: (Jul 20, 2015)
A is thrice as good as B means 3A = B. A finish the work 60 days less than B means A = B-60. So, 3(B-60) = B. 3B-180=B. 2B=180. B=90. Then, 3A=B. 3A=90. A=30. So, A's I day work is 1/30. B one day work is 1/90. Then (A+B) 1 day work together is (1/30+1/90) = 2/45. Total days they work together is. 45/2 = 22.5.

Manju Gouda said: (Jul 21, 2015)
Let us take B's work days be 'x'. Then A's will be x/3. Given difference is 60. Therefore x-x/3 = 60 on solving x = 90. Therefore B days = 90 & A = 30. A&B together will be (90*30)/(90+30) = 22.5 days.

Lins said: (Jul 31, 2015)
1:3 = x:(x+60). 1/3 = x/(x+60). So x+60 = 3x. 60 = 2x. Then x = 30.

Satyawan said: (Aug 13, 2015)
The explanation given above is very difficult to understand please try to explain the concepts as simple as possible.

Naresh said: (Aug 14, 2015)
1:3. Total 4 parts. 90/4=22.5 (one part). Here one part means A's work. Remaining 77.5 belongs to B.

Ravi Yadav said: (Aug 23, 2015)
Let A takes x days and B takes y days to complete work. In one day A completed 1/x part of work and B 1/yth. According to question 1/x = 3*1/y and y-x = 60. By solving x=30 and y= 90. So in one day both completed (1/x + 1/y) = 4/90. They can do it in = 90/4 = 45/2.

Nil said: (Aug 25, 2015)
A 1x -- = --- (RATIO OF TIME) B 3x And difference is given 60 days. 3x-1x=60. 1x = 30 days for A. 3x = 90 days for B. I don't remember but I think I have posted the another method up above long time before.

Rahul said: (Aug 25, 2015)
Can we solve such questions by LCM method? Please help.

Ramesh said: (Sep 24, 2015)

Time ratio between A and B is 1:3. A/B = 1/3------ (1). B takes thrice the time taken by A. A-B = 60 from A = B+60--- (2). BY substituting (2) in (1). Then get time taken by B to finish work in 90 days. From (1) you get time taken by A to finish work in 30 days. A's 1 day work is = 1/30. B's 1 day work is = 1/90. (A+B) 1 day's work is = (1/30+1/90) = 2/45.

Then time taken by the A and B working together is 45/2.

Anshul said: (Oct 5, 2015)
We can solve this question easily. A:B = 1:3. Difference is 60. Hence ratio becomes: A:B = 30:90 = 1:3. Here we can see diff is 60. So our answer will be 90*30/90+30 = 270/12. = 90/4 = 45/2 = 22+1/2.

Salman said: (Nov 15, 2015)

So much confusing answer given. This is basically ratio problem. 60 days less means you have to take ratio of time and solve the problem. A is thrice as better as B means. B takes thrice time compared to A. i.e Ratio of time taken by A/B = 1/3. If B takes x days then A takes x-60 days time to complete the work. i.e Ratio of time taken by A/B = x-60/x. Therefore 1/3 = x-60/x. Solve to get x = 90 therefore B takes 90 days and A takes 30 days. Daily Work of A = 1/30. Daily Work of B = 1/90. Adding work of A and B. Daily work of A and B is 4/90. So time taken for both A and B to complete the work is 90/4 = 221/2 days!

Simple as that!

Nilu said: (Dec 8, 2015)

A is thrice good as B. So, ratio of work done is 3:1 and A taken 60 days less as compare to B. Let time taken by B is x so time taken by A is x-60. So 3:1::x:x-60. 3x-180 = x. So 2x = 180 and x = 90. Time taken by B = 90 days so time taken By A is 30 days. A's one day work = 1/30 and B's one day work is 1/90. Total work done by both A and B in one day = 1/30+1/90.

= 3+1/90 = 4/90 = 2/45 = 22.5 days.

Pratim Pal said: (Jan 6, 2016)

Hi friend. This is one of easiest problem. Here given that the ratio of time taken of A and B to complete one work in individually is 1:3. So let us take A can do this work in X days and that of B is 3X days. According to conditions B took 60 days more than A. 3X-X = 60. 2*X = 60. X = 30. So time taken by B is 3*30 = 90 days and by A is 30 days. When A&B together do this work. The required time is: = 1/(1/30+1/90). = 1/((3+1)/90).

= 45/2 days.

Sagar said: (Jan 7, 2016)
Please tell me how is the difference of time is 60 days?

Sudip Purakait said: (Jan 19, 2016)
Hi @Sagar. It is mentioned in the question.

Mukunda Saini said: (Jan 27, 2016)
A is thrice as good as B. So A = 3x and B = x. A is 60 greater than B. So 3x-x = 60. 2x = 60. x = 30. A = 90 and B = 30. 1/90+1/30 = 45/2. Answer: 22 1/2.

Sravan said: (Jan 30, 2016)

Since it's mentioned that A completed 60 days less than B. We have to know there less than rate. Since it given A is thrice as good as B. That means it takes 1 day to A to do Bs 3 day work. So now we can know that A can do in (3-1) = 2 days less than B. That means A less than days for B days for 2 its 3. Similarly for 60 less day we need to multiply 2 by 30 to get 60. Since we do on 2 (A) side we have to multiply on 3 (B) side then we get. = 2x30 : 3x30. We get = 60 (for A day's lesser than B) : 90 (we got B days) that means A work days = 90-60 = 30. So 1/30 + 1/90= 0.0444 amount of work per 1 day. For 1 piece of complete work 0.4444/0.4444 = 1/0.4444 days.

That 1 piece of work done for 22.5 days by A & B together.

Bhupinder said: (Feb 4, 2016)
Good explanations thanks.

Vamshidhar said: (Feb 5, 2016)
In the explanation, said that, "If difference of time is 60 days, B takes (3/260) = 90 days. My opinion is if A can complete work in 60 days then B should complete work in 360 = 180 days but not in 90 days. Can anyone explain this part?

Ram said: (Feb 15, 2016)
Guys, this is pretty simple. Given A : B = 3 : 1, difference in time taken is 2. Let us consider it as 2 parts. Then it's also given that A can complete the work with 60 days gap to B. Hence we can equate these 2 parts to 60 days. Therefore 2 parts = 60 days. A's part is 1 parts = 30 days. B's part is 3 parts = 90 days. Rest you know. Hope you intelligent guys understand :).

Bunny said: (Apr 1, 2016)
How to do LCM?

Dipa said: (Apr 1, 2016)
3x:1x => 3x - 1x = 60. => 2x = 60. => x = 30. => 3x = 90. A+b together work = 90 * 30 / 90 + 3. => 2700 / 120 = 22.5 days.

Pari said: (Apr 18, 2016)
Thanks for giving a different solution.

Guarav said: (Apr 19, 2016)
A is thrice as good as B i.e A:B = 3:1. The ratio will be same. Now let a number of days for B be x. Thus, for A it becomes (x - 60) Now equate 3/1 = x/(x-60)(ratio of days of B to the days of A). 3x - 180 = x. x = 180/3. x = 90. No of days by B is 90. Hence days of A will be 30.

Ramya said: (Jun 3, 2016)
Thank you @Siva. It's simple to learn.

Inzamamul Haq said: (Jun 4, 2016)

Workman. A : B. 3 : 1. Time taken; A : B. 1 : 3. A) if B finish work in 30 days then, A can finish it in 10 days. Now the difference in a day is 20. B) if B finish work in 60 days then, A can finish it in 20 days. Now the difference in a day is 40. C) if B finish work in 90 days then, A can finish it in 30 days. Now the difference in a day is 60. Given question. The difference is 60 days. Hence, condition c) satisfies. A 1-day work is 1/30. B 1-day work is 1/90. A + B 1 day work is 1/30 + 1/90 = 4/90.

Days to complete the work is 90/4 => 22 1/2.

Mahesh said: (Jul 14, 2016)
Let consider B can do work in n days. 1 days work of B = 1/n. So, A = n - 60. 1 day work of A =1/ (n - 60). As given A = 3b. 1/ (n - 60) = 3 * (1/n). n = 90. B can do work in 90 days. So A can do in 30 days. Both = (1/30) + (1/90). = 22 (1/2).

Insane said: (Jul 26, 2016)
Let A be X where as b = 3x. So, 3x - x = 60. x = 30. a = 30, b = 90. Together they can do the work in 22 (1/2) days.

Priya said: (Aug 1, 2016)
Please say me any shortcut methods to solve this problem.

Anonymous said: (Sep 24, 2016)

Hello friends, I just want to clear out something and that is according to the formula given. Here the answer is not correct. There has been a mistake and that is it is wrongly solved becomes as the question goes hereby, 1) A is thrice as good as B so the ratio would be like 3:1. But it has been mentioned as 1:3 which is wrong according to my perception.

So please make it correct or give the correct sort of explanation to prove me wrong.

SscASPIRANT said: (Oct 21, 2016)
Hi guys Here is a trick to solve it. If B = 1, A = 3, Therefore efficiency is A : B = 3 : 1. Now, 60 days less means the difference of their efficiency. 2 ---> 60 1 ---> 30 Now you got 30. A = 3 * 30 = 90, B = 1 * 30 = 30, LCM = 90. Which is total work and total days = total work/total efficiency. T.D = 90/4 = 45/2 = 22 (1/2)days.

Vaishnavi said: (Nov 8, 2016)
Thanks @Sheetal it is best trick.

Mohin Uddin Mizan said: (Nov 10, 2016)
Let B takes X days to the work. Then B's 1 day's work = 1/x and A's 1/3x. ACQ, 1/x - 1/3x = 60, So, x = 1/90. As the difference is 60, so A needed 90 - 60 = 30 days. (A + B)'s 1 day's work = 1/90 + 1/30 = 2/45. So, to do the total work they need 45/2 or 22(1/2).

Soniya said: (Dec 17, 2016)

Let t1 &t2 are time taken by A and B. w1 & w2 are work done by A and B. Ratio of the time taken by A and B =1 : 3. Then, A = x, B = 3x (x is some constant). We know that t1 = t2 - 60 (A takes 60 days less than B). t2 - t1 = 60 3x - x = 60 (t1 = x, t2 = 3x) x = 30. Then t1=30 and t2 = 90. Total work done by A& B(W) = w1 + w2. W =1/t1 + 1/t2. = 1/30 + 1/90 = 2/45.

Then time taken by A&B to finish the work is 45/2days.

Dineshkumar said: (Dec 28, 2016)
Your answer is clear @Sundar, Thanks.

Udhay said: (Dec 28, 2016)
I can't understand it. Please someone help me.

Devendra Kumar said: (Dec 28, 2016)
Please tell me the easiest solution of this problem. Like LCM method.

Hari said: (Dec 30, 2016)
A:B = 3:1 efficiency. Because, A is Thrice the work as B. So, A complete the work 60 days before. Then 2---60 1--30, So to find total work we just take it as; A = 3 * 30. B = 1 * 30. Total work is 90(LCM IS 90). So, W = ED, D = 90/4 = 22.5.

BLACK said: (Jan 1, 2017)
Ratio of time taken by A & B = 1 : 3. Suppose B takes x days to finish the job. Then A takes (x-60) days. So, (x-60) : x = 1:3 x= 90. So rest are same.

@verma Ji said: (Jan 31, 2017)
Hello Friends: this shortcut formula is better to solve these type question in less time. Alternate Method: Since 'A' is 'm' times as efficient as 'B' & takes 'D' days less than 'B', then the time required to complete the job together is given by, T = m * D/(m^2 " 1) T = 3 * 60 / [(3)^2 - 1] = 180 / 8 = 22 1/2 days.

Hari. said: (Mar 17, 2017)
Thanks @Sachin.

Suresh said: (Mar 17, 2017)
A is 3 times more efficient than B, A=3B A do the work less than 60 days compared to B, A-60=B. So, we can write it as, A = 3(A+60) A = 3A+180 2A = 180 A = 90 90-60 = B B = 30.

JPV said: (Mar 21, 2017)
Ratio of no days taken to do work by and b= x : 3x. It's give that diff= 60. ie 3x-x = 60, ie x = 30. No of days taken by B=90. No of days taken by A=30. ie total no of days taken when work is done together= 1/30 +1/60, = 22 1/2.

JAY said: (Mar 21, 2017)
LET: A = 3B. where: A = 1/x and B = 1/(x+60) so; (1/x) = 3[ 1/(x+60) ] X = 30. 1/A + 1/B = 1/T 1/30 + 1/(30+60) = 1/T Then, T = 22.5 answer.

Sahil Husain said: (Mar 31, 2017)
A=3B ----------(1) A-60=B----------(2) from equation 1 & 2 3B-60 = B B=30 and A = 90 (A+B)'S 1 day work =1\90+1\30 = 2\45, So (A+B)'s work = 45\2 = 22 1\2.

Dipak said: (Apr 4, 2017)
Guys. I'm giving simple approach. 3x - x = 60 x = 30 So respective days are 90 and 30. Total days together = 30 * 90/120 = 22.5.

Dhruv said: (Apr 13, 2017)
Hi, According to me, the solution is; A= 3B + 60, So , A + B = 0 3B + 60 + B = 0 B = -15. How to get the correct answer? Please, anyone explain me.

Sambhav said: (May 4, 2017)
Hi guys. It is given that A is thrice efficient then B then the efficiency of A is 3x and that of Y is x. then no of days are For A is(60-y) and for B is y. Then total work done is constant then 3x(60-y) = x y. Then y = 45. Then total work done by A is 45 X. And rate of work of A and B will be 3x and x and if they work together the rate will be 4X. So no of days will be = 45/4.

Sasikumar said: (May 19, 2017)
Thanks @Deepti.

Esrak Ahmed Kafi said: (May 30, 2017)
Let B can do it in 3x days. So, A can do it in X days. According to Question, 3x-x = 60. So, X = 30. So, A can do it 30 days while B can do it in 90 days. Now in (1/30+1/90) days A & B can together do the work. =45/2 = 22.5 days.

Rakesh said: (Jun 13, 2017)
How 3/2? Explain.

Sumanth said: (Jun 21, 2017)
Thanks for your explanation @Indhu.

Nagesh said: (Aug 17, 2017)
Thank you for all the given explanation.

Pramod Patel said: (Aug 29, 2017)
I think the best and universal approach is this: A can do the work in X days, B takes X+60 days for same work, But (X+60)/X=3/1 as time taken by A and B is in 1:3 ratio, Solving we get X=30, A's one day work is 1/30, B's one day work is 1/90, combining their one day work we get 1/30+1/90=2/45, total time taken by them is 45/2.

Haritha said: (Aug 31, 2017)
It's a clear explanation. Thank you @Sheetal.

Tiya said: (Sep 19, 2017)
Please solve this question. If the ratio of work efficiency of A and B is 3:2. If A and B together finish a work in 5 days in how much days B alone complete the work?

Bismi Maria Jose said: (Sep 22, 2017)

It is said A is 3 time as good as B. ie. A=3*B Again given, A is able to finish a job in 60 days less than B. say, B takes x days to complete 1 work therefore A takes x-60 days to complete 1 work(same work) A's 1 day work=1/x-60 B's 1 day work=1/x. Substituting; Applying in formula, A=3B ie. 1/x-60=3/x so,x=90 x-60=30 so we got the number of days A alone and B alone worked i.e 60 and 90 1 day work of (A+B)=1 / 60 + 1 / 90 = 2/45, So,nobr of days (A+B) worked = 45/2,

Answer is option B.

Purusottam said: (Sep 27, 2017)
The answer must be 45 days. Let B does the work in x days. Now let's think about A's efficiency. As far as the question is concerned, 3100/x =100/60. So, x=180, Efficiency of A+B=100/60+100/180, = 20/9%. So 20/9...........1 1..............9/20 100..........9/20100 . =45.

Purusottam said: (Sep 27, 2017)
Yes, correct @Sugumaran.

Anupam Kumar said: (Oct 1, 2017)

Let us understand this in a much simpler way. Let the time taken by B to finish the work be X days. Then according to the question Time is taken by the A is (X-60). Work done by B in one day is (1/X), Work done by A in one day is (1/X-60), And we know that A is three times faster than B, So work done by A in one day is three times the work done by B in one day. So 3*(1/X)=(1/X-60), 3X-180=X, X=90, Therefore B takes 90 days to complete the work hence A take 30 days to complete the work, therefore together they take 1/(1/30+1/90) days, which is equal to 45/2.

Thank you all.

Saikrishna said: (Oct 22, 2017)
a b x 3x 2x=60 so x=30 total work=3*30=90 Ans=90/4=22 1/2.

Rohi said: (Oct 26, 2017)
Ratio of times taken by A and B = 1:3. Means B will take 3 times which A will do in 1 time. If difference of time is 2 days, B takes 3 days, If the difference of time is 10 days, B takes (3/2) * 10 =15 days.

Biplab Sarkar said: (Oct 30, 2017)
Here given k=3, n=60. So formula is -> kn/ (k^2-1) =3*60/ (3^2-1) =180/8=22 1/2 days.

Shaman said: (Oct 30, 2017)
Please provide the solution of if A is 5 times better than B together they complete the work in 50 min then B alone can do the work in how many minutes.

Jack said: (Oct 31, 2017)
Can anyone explain me why the step 3/2*60 used. I couldn't get the logic of finding difference as 2.

Pramod Nepal said: (Nov 6, 2017)
Let see @Shaman. A finish work in x day and B can 5x day. Then we can do A+B= 1/x +1/5x. We have A+B = 50, 50 = 5x/6 after sol x= 60 it means A can do in 60 min and B 300 min.

Nik said: (Nov 8, 2017)
How 4/90 comes?

Rizwan said: (Dec 19, 2017)
From where does this 4/90 comes? How 4?

Vishal said: (Dec 27, 2017)
I have better solution. A:B-3:1(rate). A:B-1:3(days). Diff of 2 between ratio of days which is equivalent to 60 and 230=60. Hence 30 will be multiplied to 1 and 3. And we get 30 and 90. Together days taken= 30 90/30 + 90 = 22 1/2.

Dusu Opo said: (Jan 17, 2018)
Why 60 days? Please explain.

Sherin said: (Jan 18, 2018)
Thank you @Showry.

Jiban said: (Feb 10, 2018)
Can it be in this way? B will take 180 days more than A. Then calculate for 1 day. Can anyone solve this?

Nurun Nobi Khokon said: (Jun 1, 2018)
Let A take x days So, B takes x+60 days 3x = x+60 (B took 3 times more, so to make the equation equal he have to multiply the days taken by A by 3). or, 2x = 60, or, x = 30 days. A takes 30 days and b takes 30+60 or 90 days., Now, (A+B)'s 1 day's work = (1/30+1/90) or 4/90 or 2/45, So, total days required to do the whole work, 45/2 or 22.5 days.

Kavitalodhi said: (Jun 7, 2018)
In the question clearly, say that A takes 60 days less than B. So A can do the work in B-60 days, And time ratio of A:B = 1:3, 1/3=B-x/B =>B=90,A=30. So, A and B can do the work together 1/30+1/90 =>2/45, Mix fraction of 2/45 is 22 1/2.

Mohit said: (Jun 15, 2018)
3 x 60/3^2-1 = 22 1/2.

Balaji said: (Jun 28, 2018)
Capacities of A:B=3:1. Time taken ratio of A:B=1:3. Difference of ratio in time is 2 = 60 days => A takes 30 days and B takes 90 days => 90/4=22 1/2.

Balaji said: (Jun 28, 2018)
Capacities of A:B=3:1. Time taken ratio of A:B=1:3. Difference of ratio in time is 2 = 60 days => A takes 30 days and B takes 90 days => 90/4=22 1/2.

Balaji said: (Jun 28, 2018)

Capacities of A:B=3:1. Time taken ratio of A:B=1:3.

Difference of ratio in time is 2 = 60 days => A takes 30 days and B takes 90 days => 90/4=22 1/2.

Balaji said: (Jun 28, 2018)
Capacities of A:B=3:1. Time taken ratio of A:B=1:3. Difference of ratio in time is 2 = 60 days => A takes 30 days and B takes 90 days => 90/4=22 1/2.

Rajashekar said: (Aug 9, 2018)
Shortcut of these type of problems: A&B = Difference * 'n' times / n^2 - 1. = 60*3/3^2-1 = 180/9-1. = 180/8=22.5 or 22 1/2.

VICKMA said: (Aug 11, 2018)

Here A is thrice EFFICIENT than B. A=1 B= 3 A takes 60days less than B to finish a work, This shows that if B takes to complete a work by "X" days. Then A will take X - 60 days to complete a piece of work. We know that A=1. B=3 A= X - 60 B= X (No.of day to complete a work). Cross multiply: 3(X-60)=X => 3X-180=X, -180=-2X => X= 90. WORKING TOGETHER: A+B = 1/X-60 + 1/X. We know that X = 90, A+B = 1/90-60 + 1/90, =1/30+1/90, =(3+1)/90 => 4/90 => 2/ 45. Therefore, A+B takes 45/2 days to complete a piece of work.

A+B = 22 1/2.

SWETHA said: (Aug 25, 2018)
Since A finishes the job in 60 days less, from (ii) we get: 3X - X = 60. A=30 B=90, A+B=1/30+1/90. =2/45. A and B together can do the work in 45/2=22 1/2.

Naidu said: (Sep 5, 2018)
It is a good and clear method, Thanks @Prashant.

OM PRAKASH REDDY said: (Sep 27, 2018)

NO RATIO'S. A is thrice as good as B. This implies that if B take '' T '' days to complete the work, then A takes just ''T/3" days for same amount of the work. Now coming to the second point in the question, A takes 60 days less than what B takes. T/3 = T - 60. ----> T=90, ao B takes 90 days alone which implies A takes 30 days alone to complete work.

If A and B work together then no.of days required would be (1 / (1/30)+(1/90) ) which results in 22.5days.

Parveez said: (Sep 27, 2018)

A is thrice as good as workman as B so the ratio of time taken by A and B is = 1:3. Let, A completed the work in x days. B completed the work in 3x days. A's 1-day work= 1/x and B's 1-day work= 1/3x, So, A+B 's 1-day work= 1/x+1/3x, =4/3x. So, A+B completed the work in 3x/4 days. Since, A finishes a job in 60 days less than B. therefore , 3x-x=60. x=30. therefore, Working together A+B completed the work in 3x/4 days. = 3*30/4. = 45/2.

= 22 1/2 days.

Shreya said: (Nov 13, 2018)
@All. This is the easiest & shortest!. Let a be x whereas b = 3x. So, 3x " x = 60. x = 30. therefore a = 30, b = 90. so when they work together-> 1/30+1/60 = 4/90 = 2/45. Together they can do the work in 22 (1/2) days.

Swarani said: (Dec 16, 2018)
Your explanation is easy, thanks @Showry.

Jeev said: (Mar 1, 2019)
3A = B. If 60 is less than b(then 60 is two times of a) then A=30, b = 3 * 30 = 90, a+b=1/30+1/90, 3*1/90+1/90, (3+1)/90. Where 4/90(to get days upside down). 90/4 = 22(1/2) days.

Chacha said: (Mar 3, 2019)
It's simply. 3a = b.

Manohar said: (Mar 20, 2019)
A+B = 1/60 + 1/180. A is three times more efficient than B. (So that if a takes 60 days then B takes 180 days). And therefore; 2(A+B) = 180/4 = 22 * 1/2.

Chawdharya said: (Mar 26, 2019)
A : B TIME 1/3 : 1. DAYS X-60 : X. X-60/X = 1/3, X= 90, X-60 = 30. A work efficiency = 1/90, B work efficiency = 1/30, A+B work efficiency = 1/90+1/30, = 2/45, work efficiency = work/time. work is constant,so time = 45/2. = 22.5.

Ameer said: (Apr 1, 2019)
Thank you, excellent explanation. a = 3b --> (1). a-b = 60. 3b-b = 60. 2b = 60. b = 30. If b = 30 then from 1a = 3 x 30 = 90. Now, = 1/30+1/90. = 3+1/90. = 4/90 = 2/45. = 45/2 = 22.5 days.

SAMANTH KUMAR said: (Apr 11, 2019)
Let A=X ,B=X+60 (GIVEN A TAKES 60 DAYS LESS THAN B,I CONSIDERED B TAKES 60 MORE DAYS THAN A). Now, LCM OF X,(X+60) = X(X+60), Efficiency of A=(X(X+60)) / X = X+60, Efficiency of B=(X*(X+60)) / (X+60) = X. Total work of A&B = (X(X+60))/(X+X+60), We have A=3B (GIVEN). X = 3(X+60), X = 30. Put in the equation and get the answer 45/2 =22(1/2).

Priya said: (May 16, 2019)
The solution is; A = x , B = 3x x = 3x-60 x = 30 A = 30; B = 90; 1/30 + 1/90 = 2/45 = 22.5 days.

Harsh said: (May 25, 2019)
I am not understanding anything this, please explain.

Anitha said: (Jun 8, 2019)
A:B = 1:3 2p = 60 P = 30 30 : 90 1/30 + 1/90 = 2/45 = 22.5.

Sai said: (Jun 23, 2019)

A is thrice as B, A:B=1:3. B takes 60 days more than A to complete the work. Lets consider A to complete the work in x days, therefore, B completes the same work in (x+60) days, x:(x+60). Therefore, As these are equally related to one and other; 1:3::x:(x+60). Cross multiply we get x=30 days ie A can finish the work in 30 days, Therefore B can do it in 90 days ie 3 times more days given. Therefore: (1÷30)+(1÷90).

= 22.5 days.

Tachime Sangma said: (Jul 4, 2019)
How come 4/90? I don't understand.

Meg said: (Jul 21, 2019)

First thing, the work done is always same, i.e. Work done by A = work done by B = work done by A+B. So, if A does a work in x days then B does it in 60-x days. Now, we can write A=3B So, work done by A will be = 1*x = x Work done by B will be = 3*(60-x) As we know work done remains same then x = (60-x)*3. x = 45, So, A's total time = 45. B's total time = 60-x = 60-45 = 15. So, now we can find the total time taken by A+B to complete the work as, 1/15 + 1/45 = 4/45. It's one day work of A+B so reciprocal it to get the total time taken by them.

45/4 = 22.5 days

Subhendu said: (Aug 22, 2019)
(3-1)=2------>60 1------>30 3------->90. 1's day work for A= 1/30 1's day work for b=1/90 Both 1's day work=(1/30+1/90) = 4/90. Total day = 90/4. = 22(1/2). The answer is B.

Neena said: (Aug 25, 2019)
We can simplify it. Assume if B worked for 90 days and C worked for 30 days. B's 1-day work = 1/90. A's 1-day work = 1/30. A+B = 4/90 work. ie, 90/4 = 22.5.

Yash said: (Sep 23, 2019)
(TT.D)/(T^2-1). T-EFFICIENCY. T.D-TIME DIFFERENCE. So; 360/9-1 = 22.5.

Yaswanth said: (Sep 23, 2019)
Let's assume A completes its work in x days. B completes in 3x days . since A is times efficient than B. now, their difference is 60 days. then, x-3x=60, 2x=60, x=30, A=30,B=90. So, one days work of A and B together is A+B=1/30+1/90. =4/90, =2/45, So one day work of A and B together is 2/45. So A and B can complete the work in 45/2 days. this equals to 22(1/2).

Sanishk said: (Oct 15, 2019)
What is wrong with the below step? A's 1-day work = 1/y. Then, B's 1-day work = 1/3y. Now, A completes work before 60 days compared to B. So, 1/y - 1/3y = 1/60 2/3y = 1/60 y = 40. i.e., A completes in 40 days and B completes in 120 days, Now, working together they complete in 1/A + 1/B = 1/40+ 1/120 = 1/30. So, Together they complete in 30 days.

Rohan said: (Oct 16, 2019)
A and B Work 3:1 Time 1:3 i.e. 30:90 ......multiply by 30. And also they have given that the difference between the time taken to complete the work is 60. Hence when A and B time to work together, 1/30+ 1/90 = 2/45, Defer for A and B to complete the entire work they require 45/2 which is equivalent to 22 and A half-day.

Aravind said: (Nov 19, 2019)

Hi, friends, it's a bit tricky. First, they found the time difference to do work between a and b. Because the data we have is time difference in qn for 60 days consider. Then. If a takes 1 day. B takes 3 days. So. For 2 days time difference : 3 days for b Then multiply both sides by 30 since the time difference is given For 60 days time difference: 90 days of b. I hope you all get it.

Then use ratio. A takes 30 days to complete work.

Dinesh said: (Dec 3, 2019)
Please tell how A is working 30 days. How we calculate I don't understand.

Priti said: (Dec 11, 2019)
*shortcut method**** D= no of days. n= n times as fast. Dn/n^2-1 603/3^2-1 180/9-1 180/8=90/4=22 1/2.

Abhijith said: (Dec 24, 2019)
Can someone provide a solution for this problem using percentages or the efficiency ration ?

MOSA said: (Jan 20, 2020)
Let a did this work in X days. B can do it in 3x days. X+60=3x. X=30. It means A can complete this work in 30 days and B in 90 days; Capacity of; A is 3. B is 4. A+B= 4. TIME =90/4.

Rajesh said: (Apr 1, 2020)
Work=3:1. Time 1:3. 2 part=60 (difference). 1 part=30. 130:330=30:90. He asked work of B( 90)can do by both in how many days. 90/(1+3)= 90/4=22.5 days.

Naga said: (Jun 30, 2020)

The ratio of work done by A & B= 1:3. (Because A is thrice as good as B) A' s work done = Less than 60 days than B. So take B's work done = x days---(1) Then A's work done = x-60---(2) So, 1=x-60, 3= x. So cross mutiply as per the ratio simplification. x * 1= 3(x-60), x=3x-180, 3x-x=180, x =90. As per (1) & (2) B's work done = 90 days, A's work done = 90-60 = 30 days, (A+B)'s 1 day work done = 1/30 +1/90=4/90=2/45,

Total work done = 45/2= 22 1/2 days.

Bindu said: (Jul 13, 2020)
3/2 *60, how come 3/2?

Billal Hossain said: (Jul 14, 2020)
x : 3x. 3x - x = 60, => 2x = 60, => x = 30, 1/30 + 1/90, = 4/90. = 22 (1/2).

Nirmala Rai said: (Jul 19, 2020)
Ratio of A:B=1:3(efficiency). =3:1(time will be opposite of efficiency). Time difference between A:B=2. 2 denotes =60, 1 denotes=60/2=30 A, 3 denotes =60/2*3=90 B calculate L. C. M of A &B = 90, A+B=90/4= 22(1/2)-Ans.

Rajeesh Kumar said: (Aug 7, 2020)
@All. We can easily convert it to a linear equation. Let B requires x days and forA it is y it is given,x = 3y. In the same way; X-60=Y By solving we have 2x- 180=0 :.x=90. and y=90 - 60 = 30.

Saurabh said: (Aug 12, 2020)
time diffence = 60days. A is 3 times better then b. That means A will do 3 times of work in day and B will do 1 time of A's work in 1 day difference = 2 times. Day difference = 60 1 time difference = 60/2 = 30. A will do the work in 30 days. B will do a work in 3*30 = 90days.

Atharv Pathak said: (Aug 19, 2020)
W1/w2 = d2/d1. W1 = 3w2. And d1 = d2-60. So, 3w2/w2 = d2/d2-60, d2 = 90, d1 = d2 - 60 = 90 - 60 = 30. 1/90 + 1/30 = 1/22.5. Ans 22 * 1/2.

Sagar said: (Aug 20, 2020)
Thank you for very simple answer @Malleswari.

Akshay Salekar said: (Aug 21, 2020)

Hi, friends. We know that A capability to do work is 3 times of B,ok Then the the ratio of Efficiency is A:B=3:1 And the ratio of time (days) is A:B=1:3 ...(The ratio get reverse because Efficiency and time are inversely proportional) Now, Time taken by A to complete work = (X) day & Time taken by B to complete work = (X+60) day. *We compare the ratio of time (X/X+60)=(1/3) get X = 30 ----> (1). From (1) we get A need 30 Days and B need 90 days Now take lcm of (A day and B-day). That is LCM of (30 & 90). A & B need to complete 90 work. So, the efficiency of A is (3 w/d) & B's efficiency (1w/d). When they together (A+B) = work done is (4w/d).

So (90w/(4w/d)) = 22 1/2.

Omkar Raut said: (Sep 1, 2020)
A:B = 1 : 3. Let's say A's work is x, then x : 3x. Now, 3x - x = 60. Given in question. 2x = 60, x = 30 Now,A = 30, B = 90.

Nidhu said: (Sep 12, 2020)
So, let's take the ratio as 3:1. Consider b - 60 = a. 3a - 60 = a, A = 30, 30 = b-60, B = 90. A + b = 1/30 + 1/90. = 2/45. Which is 45/2=22.5=22 1/2.

Bhairus said: (Oct 22, 2020)
A = 3B; A time : x-60; B time =x; In 1 day together work =1/(x-60) +1/x. And we also know (x-60)/x = 1/3; From this two got x = 90 and time from eq 1 is 22.5.

Dnyaneshwar said: (Nov 28, 2020)
A = 3B Suppose workdone in 1 day by 'B'= 1/n. Suppose workdone in 1 day by 'A'= 1/(n-60). We get eqn; 1/(n-60) = 3(1/n). So, n =90 days (Time taken by B to complete the work). A= 30 days. A+B = (1/30)+(1/90) = 22.5.

Sanky said: (Dec 6, 2020)
A:B = 1:3. B = 3A. Difference is 60days, therefore B - A = 60, 3A - A = 60, 2A = 60, A = 30 & thus B = 90. Now, 1/30 + 1/90 = 22.5.

Ranjana Shree said: (Mar 9, 2021)
We can simplify it. Assume if B worked for 90 days and; C worked for 30 days. B's 1-day work = 1/90. A's 1-day work = 1/30. A + B = 4/90 work. ie, 90/4 = 22.5.

Paru said: (Apr 8, 2021)
@Harsha You gave a very good explanation, thank you.

Ahamed said: (Apr 10, 2021)
Thank you all for explaining.

Apsar Khan said: (Apr 28, 2021)
If A completes the work in x days, B will do the same in 3x days. 3x - x = 60. 2x = 60. Then x = 30 and 3x = 90. (A + B) 's 1 day's work. =1/30 + 1/90. = 4/90. So, A and B together will do the work in; = 90/4. =>22 and 1/2.

Adheer said: (Jun 2, 2021)

If B completes the work in X days, then A completes the work in X-60 days. A is thrice good as workman as B then, the ratio of the time taken to finish the same work is 1:3 Then, (X-60) : X :: 1 : 3 Solving this, X = 90 Means B finish the work in 90 days and A finishes the work in 30 Days, Working together, their 1-day work, 1/90 + 1/30 = 4/90 = 2/45.

Mean working together, they finish the work in 45/2 = 22(1/2) days.

HMJ said: (Aug 14, 2021)

A=3B, A can finish the job 60 days less then B, Say, work=60. Capacity of B = (60/x) ----> 1 Cap of A = (60/x-60) ----> 2. As per the condition A=3B. Compare the above equation by putting the Capacity of A = 3 times Capacity of B. You will get x=90. Now put this x in above equations 1 and 2. You will get the cap of A = 2 and Cap of B = 0.66. Working together, Days= Work/(cap of A + cap of B). = 60/2.66,

= 22.5.

Astik Mandal said: (Aug 20, 2021)
A - 30d. B - 90d. lcm - 90(total work). Efficiency of A - 3. Efficiency of B - 1. Total Efficiency = 4 total. work/totalEfficiency=90/4=22.5.

Srikanth said: (Sep 9, 2021)
Thanks @Sundhar.

Padma said: (Oct 6, 2021)
Here a simple calculation is; A takes 1 part and B takes 3 parts. \ So A:B ratio is 1:3. total 4p.and the difference is 2,they did work in 60 days so 60p. 4p=60. p=15/1. B total working days 15*3=45. W/t is 45/2.

Sachin said: (Oct 10, 2021)
Thanks everyone.

Jeeva said: (Dec 17, 2021)
a ------ b x ------ 3x. 1/3 of the work is remaining = 1 - 1/3. = 2/3. 2/3 of the work is completed by b = 60 days. one of the work is completed by b = 60 * 3/2. b = 90. B one day work = 1/90. A one-day work = 1/30. a+b = 1/30 + 1/90. a+b = 4/90 a+b = 2/45. A and B together can do the work = 45/2.

Muhammad said: (Dec 22, 2021)
Let A's total work completion time be = n. B's total work completion time = 3n, Difference between B and A's daily work = 60. 3n - n = 60, 2n = 60. n = 30. Total daily work. =1/3n + 1/n, =1/90 + 1/30, =2/45, So total time to complete for both = 45/2 = 22.5.

HARINI said: (Mar 26, 2022)
Given; A = 3B; A = B - 60. Substitute A = 3B in 2nd equation(a=b-60). 3B = B-60 B = 30. Therefore; A = 3B = 90. A+B = (1/30 + 1/90) = 2/45. So, the answer is 22(1/2).