Question 78

Two pipes P and Q together can fill a cistern in 4 hours. When opened separately, Q will take 6 hours more than P to fill the cistern. In how much time can P alone fill the cistern?

Solution

Let pipe P take x hours to fill the cistern. Then pipe Q takes (x+6) hours to fill the same cistern.

Pipes P and Q together fill (1/x)+1/(x+6) = 1/4th of the cistern in 1 hours

$$4(x+6+x) = x(x+6)$$

$$8x+24 = x^2+6x$$

or,$$x^2-2x-24 = 0$$

or,$$(x-6)(x+4) = 0$$

or,$$x = 6.$$

A is correct choice.

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