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

Answer: (D)

18 minutes

Answer 2

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.