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Sept. 14, 2021 Aug. 7, 2022 Solution P1 can fill the tank in 8 hours while P2 can fill the tank in 12 hours therefore when Both the pumps are opened simultaneously they can fill $$\frac{1}{8}$$ + $$\frac{1}{12}$$ = $$\frac{5}{24}$$ this much of tank in an hour.Therefore Time required by P1 and P2 to fill full tank is $$\frac{24}{}$$ Hence they can fill half the tank in $$\frac{12}{5}$$ = 2.4 hours. After all the 3 pipes are opened the tank will be filled at the rate of $$\frac{1}{8}$$ + $$\frac{1}{12}$$ - $$\frac{1}{8}$$ = $$\frac{1}{12}$$ therefore for filling the remaining tank we will need 6 more hours. If supervisor was planning to come exactly when the tank is fully filled then he must come after 8.4 hours Time required by P1 and P2 to fill 1/3rd of the tank is $$\frac{24}{5*3}$$ = $$\frac{8}{5}$$ = 1.6 hours therefore supervisor will come after = 8.4 - 1.6 = 6.8 hours In 6.8 hours all the three pipe will fill $$\frac{6.8}{12}$$ = 0.56 of the capacity of tank therefore remaining tank to be filled when the supervisor comes = 1- 0.56 - 0.33 $$\approx$$ 0.1 i.e. 10% Therefore option 'C' is our answer
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Math Expert Joined: 02 Sep 2009 Posts: 86558
A cylindrical overhead tank is filled by two pumps P1 and P2. P1 can f [#permalink]
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Question Stats: Hide Show timer StatisticsA cylindrical overhead tank is filled by two pumps P1 and P2. P1 can fill the tank in 8 hr while P2 can fill the tank in 12 hr. There is a pipe P3 which can empty the tank in 8 hr. Both the pumps are opened simultaneously. The supervisor of the tank, before going out on a work, sets a timer to open P3 when the tank is half filled so that the tank is exactly filled up by the time he is back. Due to technical fault P3 opens when the tank is one-third filled. If the supervisor comes back as per the plan what percent of the tank is till empty?A. 15%B. 12%C. 10%D. 8%E. 6% Are You Up For the Challenge: 700 Level Questions _________________
Manager Joined: 26 Oct 2020 Posts: 94
A cylindrical overhead tank is filled by two pumps P1 and P2. P1 can f [#permalink] Answer C 14.28%(little variable will be because at last, I am playing with time) that attempt to reduce my time for answer the question did not work so let us stick to the standard method 1.2 hrs was the difference between 9.6-8.4 at a rate of 2 so the water left to fill the tank will be 1.2*2=2.4 that is 10% of our tank.
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Originally posted by bond001 on 03 Dec 2020, 03:59.
Intern Joined: 27 Nov 2020 Posts: 1
A cylindrical overhead tank is filled by two pumps P1 and P2. P1 can f [#permalink] Let's say the tank has a capacity of 24L Then, Rate of Pump A = 3 L/hrRate of Pump B = 2 L/hrRate of Pump C = -3 L/hrtime elapsed when the tank is halfway full(12L) = 12/(3+2) = 2.4 hrsWhen the third pump is turned on, new rate is (3+2-3) = 2 L/hrTime when the supervisor is back = (12/2)+2.4 = 8.4 HrsIf the pump switches only when a third of the tank is full(8L) then time elapsed until then = 8/5 = 1.6 hrsSince the manager returns after 8.4 hrs, the pumps have 6.8 hrs to run.also, the rate of pumps after third pump is switched on is 2 L/hr.Therefore, in 6.8 hrs the pumps will fill 13.6L (6.8x2) of the tank. Add to that 8L already filled earlier, we get 21.6L. Leaving 2.4L or 10% of the tank empty Answer: C
Math Expert Joined: 02 Aug 2009 Posts: 10477
Re: A cylindrical overhead tank is filled by two pumps P1 and P2. P1 can f [#permalink]
Bunuel wrote: A cylindrical overhead tank is filled by two pumps P1 and P2. P1 can fill the tank in 8 hr while P2 can fill the tank in 12 hr. There is a pipe P3 which can empty the tank in 8 hr. Both the pumps are opened simultaneously. The supervisor of the tank, before going out on a work, sets a timer to open P3 when the tank is half filled so that the tank is exactly filled up by the time he is back. Due to technical fault P3 opens when the tank is one-third filled. If the supervisor comes back as per the plan what percent of the tank is till empty?A. 15%B. 12%C. 10%D. 8%E. 6% The entire tank can be filled by P1 and P2 inCombined one hour work \(=\frac{1}{8}+\frac{1}{12}=\frac{5}{24}\).So, total time taken = \(\frac{1}{\frac{5}{24}}=\frac{24}{5}\)Half will get filled in \(\frac{12}{5}\), but one-third will get filled in \(\frac{8}{5}\).The remaining portion in the end will be the less work done during the time \(\frac{12}{5}-\frac{8}{5}=\frac{4}{5}\).The (negative) work done by P3 in 4/5 hrs = one hour work * 4/5 = \(\frac{1}{8}*\frac{4}{5}=\frac{1}{10}\)1/10 means 100*1/10 = 10%C _________________
Re: A cylindrical overhead tank is filled by two pumps P1 and P2. P1 can f [#permalink] 03 Dec 2020, 06:14 |
An overhead tank in the form of cuboid is filled by two pumps
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