Question

A cyclindrical water tank having a height of 6 metres has a capacity of 5,000 litres. Two pipes are filling this tank at the rate of 30 litres per second and 20 litres per second. There are two leaks in the tank. One is at a height of 3 metres and it drains water at the rate of 10 litres per second. Other is at a height of 4.5 metres and it drains water at the rate of 5 litres per second. How much time will it take to fill the empty tank?

• A. 120.24 seconds
• B. 108.62 seconds
• C. 116.96 seconds
• D. 112.48 seconds

Answer 1

The Correct Option is C

Calculation of Time to Fill the Tank 

Step 1: Calculate the Total Filling Rate

The filling rates of the two pipes are:

\[ 30 \text{ liters/second} + 20 \text{ liters/second} = 50 \text{ liters/second} \]

Step 2: Calculate the Total Draining Rate

The draining rates of the two leaks are:

\[ 10 \text{ liters/second} + 5 \text{ liters/second} = 15 \text{ liters/second} \]

Step 3: Calculate the Effective Filling Rate

The effective filling rate is the difference between the total filling rate and the total draining rate:

\[ 50 \text{ liters/second} - 15 \text{ liters/second} = 35 \text{ liters/second} \]

Step 4: Calculate the Time Required to Fill the Tank

The total capacity of the tank is 5,000 liters. Using the effective filling rate, the time required to fill the tank is:

\[ \text{Time} = \frac{5000}{35} \approx 116.96 \text{ seconds} \]

Conclusion:

It will take approximately 116.96 seconds to fill the empty tank.