Question

Two pipes A and B can fill a tank in 32 minutes and 48 minutes respectively. If both the pipes are opened simultaneously, after how much time B should be turned off so that the tank is full in 20 minutes?

• A. 14 minutes
• B. 15 minutes
• C. 16 minutes
• D. 18 minutes

Answer 1

The Correct Option is D

Let B be turned off after \( t \) minutes. The amount of water filled by A in 20 minutes:

A's rate \( = \frac{1}{32} \), B's rate \( = \frac{1}{48} \).

Water filled by A in 20 minutes: \( \frac{20}{32} \).

The amount of water filled by B in \( t \) minutes:

Water filled by B: \( \frac{t}{48} \).

The total water filled should equal 1 tank:

\[ \frac{20}{32} + \frac{t}{48} = 1. \]

Simplify:

\[ \frac{5}{8} + \frac{t}{48} = 1 \implies \frac{t}{48} = \frac{3}{8}. \]

\[ t = \frac{3}{8} \times 48 = 18. \]

Thus, pipe B should be turned off after 18 minutes.