Question

There are few taps and holes in tank. Each tap can fill empty tank in 10 minutes, while each hole can empty a full tank in 15 minutes. If there are 3 taps and 2 holes, how long would it take to fill empty tank?

Answer 1

Answer:

Short method:

The tank is filled in 10 hours. This fills 100% of the tank.

With the hole, the tank is filled in 15 hours, which is 150% of the tank. So the hole withdraws 50% water in 15 hours. (Because we only have to 100% of the tank, not more.)

So to withdraw 100% water, it will take 30 hours.

Step-by-step explanation:

Long method:

Let's assume the tank is of 30 units. (LCM of 15 and 10)

The tank fills in 10 hours, means the pipe fills 3 units per hour.

Let the hole withdraw x units of water per hour.

Hence the net number of units filled in one hour is: 3-x.

We know it takes 15 hours to fill 30 units when the rate is (3-x) units.

Hence, 30/(3-x) = 15. So we get x as 1 unit.

So to empty a filled tank it will take 30/1 i.e. 30 hours.