Multiple choice

A cylindrical overhead 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. The supervisor of the tank, before going somewhere, opens both the pumps simultaneously and also 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 a technical fault, P3 opens when the tank is one-third filled. What percent of the tank is still empty if the supervisor comes back as per plan?

  1. 25%

  2. 12%

  3. 10%

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P1+P2 fill rate = 1/8 + 1/12 = 5/24. P3 empty rate = 1/8. When P3 opens, net rate = 5/24 - 1/8 = 2/24 = 1/12. The tank is 1/3 full, so 2/3 remains. Time to fill 2/3 at 1/12 rate is 8 hours. Total time = (1/3)/(5/24) + 8 = 1.6 + 8 = 9.6 hours. At 9.6 hours, the tank is full. If P3 opened at 1/2, it would have been full. The fault causes 10% empty.

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