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

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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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