SSC CGL 2024 PYQ — Question 72

The correct answer is option 1 i.e.  14$\frac{2}{3}$.

Let the tank's capacity = 60 (LCM of 20 and 30)

Efficiency of pipe A = 60/20 = 3

Efficiency of pipe B = 60/30 = 2

The tank is one-third full. So, remaining capacity = 60 × (2/3) = 40

The leak removes 1/4 of the water supplied by both pipes.

Leakage rate = (1/4) × (3 + 2) = 5/4

Effective rate = 3 + 2 - (5/4) = 15/4

Time required to fill one-third of tank = 20/(3 + 2) = 20/5 = 4 hours

Time required to fill remaining part of tank = 40/(15/4) = 32/3 = $10\frac{2}{3}$ hours

Total time = 4 + $10\frac{2}{3}=14\frac{2}{3}$ hours

Therefore, the total time taken to fill the tank is $14\frac{2}{3}$ days.