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# Arithmetic Aptitude :: Pipes & Cistern

## 4. 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?

Explanation :

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

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

.'. 1/x + 1/(x + 6) = 1/4

=> (x + 6 + x)/x(x + 6)= 1/4

=> x^2 - 2x - 24 = 0.

=> (x -6)(x + 4) = 0.

=> x = 6. [neglecting the negative value of x]