Question

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 hr
• B. 2 hrs
• C. 6 hrs
• D. 8 hrs
• E. 4 hrs

Answer 1

The correct option is C

6 hrs

Let the cistern be filled by pipe A alone in x hours.

Then, pipe B will fill it in (x + 6) hours.

$\begin{array}{c}\therefore \frac{1}{x}+\frac{1}{\left(x+6\right)}=\frac{1}{4}\\ \frac{x+6+x}{x\left(x+6\right)}=\frac{1}{4}\\ x^2-2x-24=0\\ \left(x-6\right)\left(x+4\right)=0\\ x=6\left[neglectingthe-vevalueofx\right]\end{array}$