# Arithmetic Aptitude :: Pipes & Cistern

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**Discussion**

## 6. Pipe A can fill a cistern in 6 hours less than Pipe B. Both the pipes together can fill the cistern in 4 hours. How much time would A take to fill the cistern all by itself?

**Answer:**

**Option C**

**Explanation :**

Let's assume time required by Pipe A to fill the cistern = X hours

So Time required by Pipe B to fill the cistern = (X + 6) hours

? Both Pipes (A+B) can fill cistern in 1 hour = [1/X + 1/(X + 6)]

Given Both pipe fill the cistern in 4 hours

=> [1/X + 1/(X + 6)] = 1/4 => [(X+6) + X]/(X+6)*x = 1/4

4X + 24 + 4X = X2 + 6x

X2 - 2X - 24 = 0

(X-6)(X+4) = 0

=> A can fill cistern in 6 hours.