A cistern will be filled in 9 hrs, but becoz of an outlet it is filled in 10 hrs, if the cistern is filled, then how much time the outlet takes to empty the cistern.

To solve this problem, we need to analyze the rates at which the cistern is filled and emptied. Let's break it down step by step.

Understanding the Filling and Emptying Rates

First, we know that the cistern can be filled in 9 hours. This means that the filling rate of the inlet is:

• Filling rate of the inlet = 1 cistern / 9 hours = 1/9 cistern per hour

However, due to the outlet, the cistern takes longer to fill—specifically, 10 hours. This means that the effective filling rate, considering the outlet, is:

• Effective filling rate = 1 cistern / 10 hours = 1/10 cistern per hour

Calculating the Outlet's Rate

Now, we can find the rate at which the outlet empties the cistern. The effective filling rate is the difference between the filling rate of the inlet and the emptying rate of the outlet. Let's denote the emptying rate of the outlet as "E" (in cisterns per hour).

We can set up the following equation:

• Filling rate of the inlet - Emptying rate of the outlet = Effective filling rate
• (1/9) - E = (1/10)

Solving for the Outlet's Rate

To find E, we can rearrange the equation:

• E = (1/9) - (1/10)

To perform this subtraction, we need a common denominator. The least common multiple of 9 and 10 is 90. Thus, we convert the fractions:

• (1/9) = 10/90
• (1/10) = 9/90

Now we can substitute these values back into the equation:

• E = (10/90) - (9/90) = 1/90

Finding the Time to Empty the Cistern

The emptying rate of the outlet is 1/90 cisterns per hour, which means the outlet takes 90 hours to empty the entire cistern. Therefore, the time taken by the outlet to empty the cistern is:

• 90 hours

In summary, the outlet will take 90 hours to completely empty the cistern. This problem illustrates the importance of understanding rates and how they interact when multiple processes are involved.