Sump Fill and Leak Drain Time Calculation
First, determine the rate at which the pipe fills the sump.
- Pipe fill time = 2 hours.
- Pipe filling rate ($R_p$) = $\frac{1}{2}$ sump/hour.
Next, calculate the combined rate of filling when the leak is present.
- Time taken with leak = $2 \frac{1}{3}$ hours = $\frac{7}{3}$ hours.
- Combined filling rate ($R_{p+l}$) = $\frac{1}{\text{Time taken with leak}} = \frac{1}{7/3} = \frac{3}{7}$ sump/hour.
Calculate the rate at which the leak drains the water.
- Leak draining rate ($R_l$) = Pipe filling rate ($R_p$) - Combined filling rate ($R_{p+l}$)
- $R_l = \frac{1}{2} - \frac{3}{7}$
- $R_l = \frac{7}{14} - \frac{6}{14} = \frac{1}{14}$ sump/hour.
Finally, calculate the time required for the leak alone to drain the full sump.
- Leak drain time ($T_l$) = $\frac{\text{Volume of sump}}{\text{Leak draining rate}}$
- $T_l = \frac{1 \text{ sump}}{1/14 \text{ sump/hour}} = 14$ hours.
Based on the calculations using the provided numbers, the leak would take 14 hours to drain the sump. The correct answer provided is Option C: 8 hours.
Similar Questions
- Three pipes of diameters 2 cm, 3 cm and 4 cm are running together to fill a cistern. The smallest pipe alone can fill the cistern in 232 minutes. The amount of water flowing in each pipe is proportional to the square of its diameter. The time (in minutes) taken by all pipes running together to completely fill the cistern is:
- Two pipes A and B can fill an empty cistern in 18 and 27 hours, respectively. Pipe C can drain the entire cistern in 45 hours when no other pipe is in operation. Initially, when the cistern was empty Pipe A and Pipe C were turned on. After a few hours Pipe A was turned off and Pipe B was turned on instantly. In all, it took 55 hours to fill the cistern. For how many hours was Pipe B turned on?
- Pipes A, B and C are attached to an empty cistern. While the first two can fill the cistern in 4 and 10 hours, respectively, the third can drain the cistern, when filled, in 6 hours. If all the three pipes are opened simultaneously when the cistern is half-full, how many hours will be needed to fill the cistern?
Important Questions from Pipe and Cistern
A pipe can fill a cistern in 20 minutes where as the cistern when full can be emptied by a leak in 28 minutes. When both are opened, The time taken to fill the cistern is:
‘A’ pipe can empty a tank in 20 minutes. The second pipe ‘B’ has a diameter twice as that of ‘A’. If both A & B pipe are attached to the tank how much time will be required to empty the tank?
Pipes A and B can empty a full tank in 16 hours and 24 hours, respectively. Pipe C alone can fill the empty tank in 4 hours. If A, B and C are opened together, the tank will be 35% full after :
Pipes A and B can fill a tank in 36 minutes and 45 minutes, respectively. Both these pipes were opened simultaneously. After 20 minutes, a leak at the bottom of the tank was spotted which was immediately sealed. The tank was full in another 15 minutes. The leak alone can empty the full tank in:
A cistern has a leak which would empty it in 6 hours. A tap is turned on which admits 10 litres of water per minute into the cistern. When it is full it is now emptied in 10 hours. What is the capacity (in litres) of the cistern?
