A water tap A takes 7 minutes more than water tap B for filling up a tank with water. The tap A takes 16 minutes more than the time taken by both the taps together to fill the tank. find the time each tap would alone take to fill the tank.

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28 minutes, 21 minutes.

18 minutes, 1 minutes

22 minutes, 20 minutes

8 minutes, 10 minutes

answer is A.

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Detailed Solution

Supoose time taken by A to fill tank = x minutes
Then the time taken by tap B=(x−7)
Time taken by both tap A and tap B together,
=(x-16)
Suppose capacity of tank = C
Tap A speed=

\frac{C}{x}

Tap

B speed = \frac{C}{x - 7}

Tap A + tap B speed = \frac{C}{x} + \frac{C}{(x - 7)}

Now, by given condition,

\begin{matrix} (x - 16) = \frac{C}{\frac{C}{x} + \frac{C}{(x - 7)}} \\ \frac{1}{(x - 16)} = \frac{1}{x} + \frac{1}{(x - 7)} \\ (x - 16) (2 x - 7) = x^{2} - 7 x \\ x^{2} - 32 x + 112 = 0 \\ x - 28) (x - 4) = 0 \\ x = 4 or 28 \end{matrix}

If x = 4 then x−7=−3 (which is not possible)
Thus, time taken by tap A,
x=28 minutes
Time taken by tap B
x-7=28−7
x-7=21 minutes.
Correct option is 1.

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