a) 1 hours
b) 2 hours
c) 6 hours
d) 8 hours
Answer: c
Explanation: Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours
$$\eqalign{
& \frac{1}{x} + \frac{1}{{ {x + 6} }} = \frac{1}{4} \cr
& \frac{{x + 6 + x}}{{x\left( {x + 6} \right)}} = \frac{1}{4} \cr
& {x^2} – 2x – 24 = 0 \cr
& \left( {x – 6} \right)\left( {x + 4} \right) = 0 \cr
& x = 6\,{\kern 1pt} {\kern 1pt} \left[ {{\text{neglecting the negative value of }}x} \right] \cr} $$
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