There are two pipes to fill a tank. Together, they can fill the tank in 15 minutes. If one pipe can fill the tank in one and a half times as fast as the other, the faster pipe alone can fill the tank in:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 25 minutes.
Let the time taken by the slower pipe to fill the tank alone as x minutes.
Then the faster pipe, which can fill the tank one and a half times as fast as the slower pipe, would take x/1.5 = 2x/3 minutes to fill the tank alone.
Since both pipes together can fill the tank in 15 minutes, their combined rate of filling the tank = 1/15 (per minute)
The rate of the slower pipe is 1/x (tanks per minute), and the rate of the faster pipe is 1/(2x/3) = 3/2x
So, their combined rate
⇒ 1/x + 3/2x = 1/15
⇒ (1 + (3/2))/x = 1/15
⇒ (5/2)/x = 1/15
⇒ 5/2x = 1/15
⇒ 2x = 75
⇒ x = 37.5 minutes
Since the faster pipe fills the tank in 2x/3 = (2 × 37.5)/3 = 75/3 = 25 minutes
Thus,
The faster pipe alone can fill the tank in 25 minutes.