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Bunuel
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A cylindrical overhead tank is filled by two pumps P1 and P2. P1 can f 02 Dec 2020, 12:15
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C
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95% (hard)

Question Stats:

38% (03:13) correct 62% (03:17) wrong based on 60 sessions

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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%

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A cylindrical overhead tank is filled by two pumps P1 and P2. P1 can f Updated on: 03 Dec 2020, 07:31
Originally posted by bond001 on 03 Dec 2020, 04:59.
Last edited by bond001 on 03 Dec 2020, 07:31, edited 1 time in total.
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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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A cylindrical overhead tank is filled by two pumps P1 and P2. P1 can f 03 Dec 2020, 06:45
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Let's say the tank has a capacity of 24L
Then, Rate of Pump A = 3 L/hr
Rate of Pump B = 2 L/hr
Rate of Pump C = -3 L/hr
time elapsed when the tank is halfway full(12L) = 12/(3+2) = 2.4 hrs
When the third pump is turned on, new rate is (3+2-3) = 2 L/hr
Time when the supervisor is back = (12/2)+2.4 = 8.4 Hrs

If the pump switches only when a third of the tank is full(8L) then time elapsed until then = 8/5 = 1.6 hrs
Since 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
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A cylindrical overhead tank is filled by two pumps P1 and P2. P1 can f 03 Dec 2020, 07:14
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Bunuel
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%
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The entire tank can be filled by P1 and P2 in
Combined 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
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A cylindrical overhead tank is filled by two pumps P1 and P2. P1 can f 21 Feb 2026, 06:41
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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?

Work done by pump P1 in 1 hour = 1/8
Work done by pump P2 in 1 hour = 1/12
Work done by pump P3 in 1 hour = -1/8

Time taken for the tank to be half filled = (1/2)/(1/8+1/12) = 2.4 hours
Time for the tank to be filled after it is half filled and P3 is opened = (1/2)/(1/8+1/12-1/8) = 6 hours
Total time for the supervisor to return after initially opening P1 & P2 simultaneously = 2.4 + 6 = 8.4 hours

Time taken for the tank to be 1/3 filled = (1/3)/(1/8+1/12) = 1.6 hours
Tank filled in 8.4-1.6= 6.8 hours with all pumps working = 6.8(1/8+1/12-1/8) = 6.8/12 = 68/120= 17/30
Total tank filled = 1/3 + 17/30 = 27/30 = 9/10 = 90%
Tank empty = 100% - 90% = 10%

IMO C
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