Question

Pipes A and B running together can fill a cistern in 6 minutes. If B takes 5 minutes more than A to fill the cistern, then the times in which A and will fill the cistern separately will be respectively

• A. 15 minutes, 20 minutes
• B. 15 minutes, 10 minutes
• C. 10 minutes, 15 minutes
• D. 25 minutes, 20 minutes

Answer 1

The Correct Option is C

Assume the time taken by A alone to fill the cistern be \(t\ minutes\)

So, the time taken by B will be \((t + 5)\ minutes\)

From the question, we k now that

\(\frac{1}{t} + \frac{1}{t + 5} = \frac{1}{6}\)

\(\frac{t + t + 5}{t(t+5)} = \frac{1}{6}\)

= \(12t + 30 = t^2 + 5t\)

= \(t^2 - 7t - 30 = 0\)

= \((t - 10)(t + 3) = 0\)

So, the value of \(t\) can be 10 and -3

Time taken cannot be negative so, \(t = 10\ minutes\)

The correct option is (C): 10 minutes