Question

8 taps are fitted to a water tank. Some of them are water taps to fill the tank, and the remaining are outlet taps used to empty the tank. Each water tap can fill the tank in 12 hours, and each outlet tap can empty it in 36 hours. On opening all the taps, the tank is filled in 3 hours. Find the number of water taps.

Answer 1

The number of water taps can be found by setting up and solving an equation that relates the rates of filling and emptying the tank. The value of 'x' that satisfies this equation will give the number of water taps.

Step-by-step explanation:

Let's assume there are 'x' water taps. Since each water tap fills the tank in 12 hours, the rate of filling the tank by each water tap is 1/12 tank per hour. Similarly, let's assume there are 'y' outlet taps. Since each outlet tap empties the tank in 36 hours, the rate of emptying the tank by each outlet tap is 1/36 tank per hour.

When we open all the taps, the combined rate of filling the tank is the sum of the rates of filling by each water tap minus the sum of the rates of emptying by each outlet tap:

1/12x - 1/36y = 1/3 (since the tank is filled in 3 hours)

To find the number of water taps, we need to find the value of 'x' that satisfies this equation. We can then substitute 'x' into the equation to find the number of outlet taps 'y'.