Question 59

Two taps P and Q take 60 minutes and 40 minutes to fill a cistern separately. If tap Q is open for the first half time and aloneis open for the remaining time, how longwill it take to fill the cistern?

Solution

Let say, total time taken by them to fill the tank is x min.

Q :

Q fills in $$\frac{x}{2}$$ min = $$\frac{x}{2}\times\frac{1}{40}=\frac{x}{80}.$$

P:

P fills in $$\frac{x}{2}$$ min = $$\frac{x}{2}\times\frac{1}{60}=\frac{x}{120}.$$

So,

$$\frac{x}{80}+\frac{x}{120}=1$$

or, $$\frac{\left(2+3\right)x}{240}=1.$$

or, $$x=\frac{240}{5}=48.$$

D is correct choice.

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