Question

Fill pipe A is 3 times faster than second Fill pipe B and takes 32 minutes less than Fill pipe B. When will the cistern be full if both pipes are opened together?

• A. 25 minutes
• B. 24 minutes
• C. 30 minutes
• D. 12 minutes

Hint:

When solving work problems, always express individual rates clearly before summing them.

Answer 1

The Correct Option is D

Let the time taken by pipe B alone be \( x \) minutes. Since pipe A is 3 times faster, it takes: \[ \frac{x}{3} \text{ minutes} \] Given that A takes 32 minutes less: \[ \frac{x}{3} = x - 32 \] Solving for \( x \): \[ x - \frac{x}{3} = 32 \] \[ \frac{2x}{3} = 32 \] \[ 2x = 96 \] \[ x = 48 \] Thus, pipe B alone takes 48 minutes, and pipe A alone takes: \[ \frac{48}{3} = 16 \text{ minutes} \] Their rates of filling are: \[ \frac{1}{48}, \quad \frac{1}{16} \] Total rate when both work together: \[ \frac{1}{48} + \frac{1}{16} = \frac{4}{48} = \frac{1}{12} \] Time to fill: \[ 12 \text{ minutes} \]