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There are two inlet pipe in the tank which can fill the tank in 15 and 20 hours respectively. There are two leaks in the tank too, having same efficiency one at the bottom of the tank and other at 3/4th height of the tank. Find the time in which the tank will get filled, if the bottom leak can empty the tank in 30 hours.

There are two inlet pipe in the tank which can fill the tank in 15 and 20 hours respectively. There are two leaks in the tank too, having same efficiency one at the bottom of the tank and other at 3/4th height of the tank. Find the time in which the tank will get filled, if the bottom leak can empty the tank in 30 hours. Correct Answer 14 hours

Suppose the capacity of tank = 60 units (LCM of 15, 20 & 30)

∴ Efficiency of inlet pipe 1 = 60/15 = 4

Efficiency of inlet pipe 2 = 60/20 = 3

Efficiency of each leak = 60/30 = 2

Since one leak is at the bottom of the tank and other at 3/4th height of the tank;

∴ 2nd leak will not work unit the tank is 3/4th full.

∴ Time in which the tank will get 3/4th full (45 units) = 45/(4 + 3 – 2) = 9 hours

Now remaining 15 units is to be filled with both the leaks working:

∴ Time in which the remaining 15 units get filled = 15/(4 + 3 – 2 – 2) = 5 hours

∴ Total time to fill the tank = 9 + 5 = 14 hours

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