Pipe A can fill a tank three times faster than pipe B. If both pipes A and B are running together, they can fill the tank in 12 minutes, then the time taken by pipe B alone to fill the tank is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 48 minutes
Let the rate of pipe B be $r$ tanks/minute. Then pipe A's rate is $3r$ tanks/minute.
Together, rate of A + B = $3r + r = 4r$
Time to fill the tank together: 12 minutes
So, $(\text{Rate}) \times (\text{Time}) = 1$ tank
$4r \cdot 12 = 1 \Rightarrow 48r = 1 \Rightarrow r = \frac{1}{48}$
Time taken by pipe B alone:
$\text{Time} = \frac{1}{r} = 48$ minutes