Question

A tank is fitted with two taps A and B of different size. If both the taps are opened simultaneously it takes 4 hours to fill the tank. If only tap A is opened for 1 hour and then only tap is opened for 4 hours the tank becomes half. Find the time taken by tap B alone to fill the tank.

A 6 hours

B 8 hours

C 12 hours

D 14 hours

Answer 1

Answer on Question #42729– Math – Linear Algebra

Question:

A tank is fitted with two taps A and B of different size. If both the taps are opened simultaneously it takes 4 hours to fill the tank. If only tap A is opened for 1 hour and then only tap B is opened for 4 hours the tank becomes half. Find the time taken by tap B alone to fill the tank.

A 6 hours

B 8 hours

C 12 hours

D 14 hours

Solution:

Let $x$ is the rate of filling the tank with tap A and $y$ is the rate of filling the tank with tap B.

Then $4x + 4y = 1$ and $x + 4y = 1/2$. Solving this system of linear equations we get $x = 1/6$, $y = 1/12$.

So, the time taken by tap B alone to fill the tank is 12 hours.

Answer. C 12

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