Question: A cylindrical tank is filled by two pumps P1 and P2. P1 can fill the tank in 8 hours while P2 can fill the tank in 12 hours. There is a pipe P3 which can empty the tank in 8 hours. 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?

1. 15%
2. 12%
3. 10%
4. 8%
5. 6%

“A cylindrical tank is filled by two pumps P1 and P2. P1 can fill the tank in 8 hours while P2 can fill the tank in 12 hours. There is a pipe P3 which can empty the tank in 8 hours. 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?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:
Approach Solution (1):

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 hours 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.

Correct option: C
Approach Solution (2):
Let’s say the tank has a capacity of 24 L
Then the 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 hours
If the pump switches only when a third of the tank is full (8L) then the time elapsed until then = 8/5 = 1.6 hours
Since the manager returns after 8.4 hours, the pumps have 6.8 hours to run.
Also, the rate of pumps after the third pump is switched on is 2 L/hr
Therefore, in 6.8 hours the pumps will fill 13.6 L of the tank
Add that 8L already filled earlier, we get 21.6 L. leaving 2.4 L or 10% of the tank empty

Correct option: C

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