Correct Answer - Option 3 : 48 hours

**Given:**

Pipe A fills in 12 hours.

Leakage empty the tank in 16 hours

Formula Used:

Capacity of cistern = LCM of time taken by pipes to fill the cistern

Capacity of cistern = Efficiency of pipe × Time taken by Pipe to fill the cistern

Time taken by Pipe to fill the Cistern = Capacity of Cistern/Efficiency of pipe

**Calculation:**

Capacity of a tank = LCM of 12 hours, and 16 hours

⇒ Capacity of a tank = 48 units

Efficiency of pipe = Capacity of cistern/Time taken by Pipe to fill the cistern

⇒ Efficiency of pipe_{A} = 48/12

⇒ Efficiency of pipeA = 4 units/hour

Efficieny of Leakage = Capacity of cistern/Time taken by Leakage to empty the cistern

⇒ Efficieny of Leakage = 48/16

⇒ Efficiency of Leakage = 3 units/hour

Efficiency when Pipe and Leakage works together,

⇒ Efficiency of pipeA – Efficiency of Leakage

⇒ Efficiency when Pipe and Leakage works together = 4 – 3

⇒ Efficiency when Pipe and Leakage works together = 1 unit/ hour

Time taken by Pipe and Leakage = Capacity of cistern/Efficiency

⇒ Time taken by Pipe and Leakage = 48/1

⇒ Time taken by Pipe and Leakage = 48 hours

**∴ Time taken by Pipe A to fill the tank is 48 hours.**