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1. Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?

A. 1 hour

B. 2 hours

C. 6 hours

D. 8 hours

Solution:

Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours

\begin{aligned} ∴ \frac{1}{x} + \frac{1}{x + 6} = \frac{1}{4} \\ \Rightarrow \frac{x + 6 + x}{x (x + 6)} = \frac{1}{4} \\ \Rightarrow x^{2} - 2 x - 24 = 0 \\ \Rightarrow (x - 6) (x + 4) = 0 \\ \Rightarrow x = 6 [neglecting the negative value of x] \end{aligned}

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