Option 3 : 56

**Given:**

Time taken by the first pipe to fill the tank = 14 hours

Time taken by the second pipe to fill the tank = 16 hours

**Calculation:**

Part filled by both pipes in 1 hour = (1/14 + 1/16)

⇒ 15/112^{th}

The whole tank is filled in 112/15 hr

Due to leakage total time taken = (112/15) + (32/60)

⇒ 8 hrs

Part emptied by leakage in 1 hr = {(1/14) + (1/16) - (1/8)}

⇒ 1/112^{th}

Time taken by the leakage to empty the whole tank = 112 hrs

Now, time taken by the leakage to empty the half of tank = 112/2

⇒ 56 hrs

**∴ The required time to empty the half of the tank is 56 hrs.**