SSC CGL 2024 PYQ — Question 71

The correct answer is option 4 i.e. 28 min.

Given that, time taken by two pipes together = 20 minutes

Efficiency of faster pipe = $2{1 \over 2}$ times efficiency of slower pipe

Let the efficiency of slower pipe be x units/min.

⇒ Efficiency of faster pipe = ${5 \over 2}x$ units/minute

Let the total work to be done be 140 units.

⇒ Efficiency of both pipes = $140 \over 20$ = 7 units/min

Now, x + ${5 \over 2}x$ = 7

⇒ 7x = 14

⇒ x = 2

Efficiency of faster pipe = ${5 \over 2}x$ 

⇒ ${5 \over 2} \times 2$ = 5 units/min

Time taken by faster pipe to fill the tank = $140 \over 5$ = 28 minutes

Hence the faster pipe alone can fill the tank in 28 min.