Question

Pipe A fills the tank in 12 hours. After some days a leakage occurs at the bottom of the same tank and it can empty the fully filled tank in 16 hours then find the number of hours required to fill the tank when pipe A is open. 
1. 24 hours
2. 36 hours 
3. 48 hours
4. 60 hours

Answer 1

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.