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
Correct Answer: 6 hours
Let the cistern be filled by pipe A alone in x hours.Then, pipe B will fill it in (x + 6) hours
$$\eqalign{ & \therefore \frac{1}{x} + \frac{1}{{ {x + 6} }} = \frac{1}{4} \cr & \Rightarrow \frac{{x + 6 + x}}{{x\left( {x + 6} \right)}} = \frac{1}{4} \cr & \Rightarrow {x^2} - 2x - 24 = 0 \cr & \Rightarrow \left( {x - 6} \right)\left( {x + 4} \right) = 0 \cr & \Rightarrow x = 6\,{\kern 1pt} {\kern 1pt} \left \cr} $$
