A pipe can fill a tank in 15 hrs.The tank develops a hole and 10%of water leaks out. The pipe will now fill the tank in

Let's solve this problem step by step.

### Step 1: Determine the original rate of filling the tank.
- The pipe can fill the tank in 15 hours.
- Therefore, the rate at which the pipe fills the tank is \(\frac{1}{15}\) of the tank per hour.

### Step 2: Calculate the impact of the leak.
- Since 10% of the water leaks out, the effective amount of water that remains in the tank after filling is \(100\% - 10\% = 90\%\) of the water.
- This means that 90% of the water is retained, so the effective rate at which the tank is filled is reduced to \(90\%\) of the original filling rate.

### Step 3: Adjust the rate based on the leak.
- The new effective filling rate is \(90\%\) of \(\frac{1}{15}\), which is \(\frac{90}{100} \times \frac{1}{15} = \frac{9}{150} = \frac{3}{50}\) of the tank per hour.

### Step 4: Calculate the new time to fill the tank.
- The time required to fill the tank at this new rate is the reciprocal of the effective filling rate.
- Therefore, the time required to fill the tank is \(\frac{1}{\frac{3}{50}} = \frac{50}{3}\) hours.

### Final Answer:
\[
\frac{50}{3} \text{ hours} \approx 16.67 \text{ hours}
\]

So, the pipe will now fill the tank in approximately **16.67 hours**.

Would you like further details or have any questions? Here are some related questions:

1. What would happen if the leak was larger, say 20%?
2. How would the filling time change if the pipe could fill the tank in 10 hours instead of 15?
3. What would be the filling time if the leak only caused 5% of water to escape?
4. How long would it take to fill the tank if there were no leak but the pipe's flow rate was halved?
5. What if there were two identical pipes working together? How would that affect the filling time?

**Tip:** Always consider how changes in variables like leak percentage affect overall rates in problems involving rates of work.

Learn how to calculate the time required to fill a tank when a leak affects the filling rate. Detailed step-by-step solution involving rates, percentages, and time calculations. Suitable for advanced high school students and beyond.

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