Question 36

A tank is connected with both inlet pipes and outlet pipes. Individually, an inlet pipe can fill the tank in 7 hours and an outlet pipe can empty it in 5 hours. If all the pipes are kept open, it takes exactly 7 hours for a completely filled-in tank to empty. If the total number of pipes connected to the tank is 11, how many of these are inlet pipes?

Solution

Let the number of inlet pipes be x, then the number of outlet pipes will be 11-x.

The rate of emptying the tank is more than filling the tank if all the pipes are kept opened.

$$\frac{11-x}{5}$$ - $$\frac{x}{7}$$ = $$\frac{1}{7}$$

Solving, 12x =72,Hence x = 6

Therefore, the number of inlet pipes is 6.

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