A, B and C can do a piece of work in 12, 15 and 20 days respectively. How long will they take to do it working together?
A can do a piece of work in 12 days
B can do the same work in 15 days
C can do the same work in 20 days
∴ A's 1 day's work = `1/12`
B's 1 day's work = `1/15`
C's 1 day's work = `1/20`
∴ (A + B + C)'s together 1 day's work
`= 1/12 + 1/15 + 1/20`
`= (5 + 4 + 3)/60 = 12/60 = 1/5`
∴ they can do the work in 5 days.
Concept: Relation Between Speed, Time and Distance
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Question 5 Exercise 7(C)
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Answer:
Solution:
A can do a piece of work in 12 days
B can do the same work in 15 days
C can do the same work in 20 days
∴ A’s 1 day’s work = \frac{1}{12}
B’s 1 day’s work = \frac{1}{15}
C’s 1 day’s work = \frac{1}{20}
∴ (A+B+C)’s together 1 day’s work = \frac{1}{12}+\frac{1}{15}+\frac{1}{20}=\frac{5+4+3}{60}=\frac{12}{60}=\frac{1}{5}
∴ They can do the work in 5 day
Video transcript
"follow students let's read the question a b and c can do a piece of work in 2015 and 20 days respectively how long will they take to do it working together so when we have this question this question belongs to which chapter work in time right now how do we start so start solving this if a can complete its total work in 12 days therefore in one day a can do how much work 1 by 12 very good similarly b can completely total work in 15 days therefore b's one day work is very nice that'll be one by 15. then c completes his total work in 20 days quickly write it in your notebook so c's one day work will 1 be 20. great now in the question it is asked how long will they take if they all are working together so when we have such type of questions what do we do we simply sum up the work done by each one of them so it will be a plus b plus c's one day work right so what are we going to get we will have 1 by 12 plus 1 by 15 plus 1 by 20 and we know the lcm are 15 12 and 20 is very good 60 so we get 5 plus 4 plus 3 which will give us 12 by 60 great and making it in its lowest form we have 1 by 5. so what do we get finally if a b and c work together then they will be able to complete this work in five days which is your answer great thank you"
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Given:
A and B can do a work in 12 days, B and C in 15 days, and C and A in 20 days.
Calculations:
According to the question,
A and B can do the work in 12 days
so, (A + B)’s one day’s work = 1/12
Similarly, (B + C)’s one day’s work = 1/15
and (C + A)’s one day’s work = 1/20
On adding all three,
2(A + B + C)’s one days’ work = (1/12) + (1/15) + (1/20)
⇒ (5 + 4 + 3)/60 = 12/60 = 1/5
⇒ (A + B + C)’s one days’ work = 1/10
A, B and C together can finish the whole work in 10 days.
A, B, and C together can finish twice the whole work in 20 days.
∴ the correct answer is 20 days.
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