Arithmetic

Time & Work

Medium

applied

Two pipes can fill a cistern in 8 and 12 hours respectively. The pipes are opened simultaneously, and it takes 12 minutes more to fill the cistern due to leakage. If the cistern is full, what will be the time taken by the leakage to empty it?

84 hours

72 hours

108 hours

120 hours

✅ Correct Option: 4

If Pipe 1 fills the cistern in 8 hours, it fills $\frac{1}{8}$ of the cistern in 1 hour.

If Pipe 2 fills the cistern in 12 hours, it fills $\frac{1}{12}$ of the cistern in 1 hour.

Pipe 1's rate $= \frac{1}{8}$ cistern per hour

Pipe 2's rate $= \frac{1}{12}$ cistern per hour

When both pipes work together, their rates are added:

Combined rate $= \frac{1}{8} + \frac{1}{12}$

$= \frac{3}{24} + \frac{2}{24}$

$= \frac{5}{24}$ cistern per hour

Time without leakage $= 1 \div \frac{5}{24}$

$= \frac{24}{5}$ hours

$= 4.8$ hours

$= 4$ hours $48$ minutes

The leakage adds 12 more minutes to the filling time.

Time with leakage $= 4$ hours $48$ minutes $+ 12$ minutes

$= 5$ hours

Let the leakage empty the cistern in $x$ hours.

Leakage rate $= \frac{1}{x}$ cistern per hour

Net rate with leakage $= \frac{5}{24} - \frac{1}{x}$

Since it takes 5 hours to fill with leakage:

$1 \div \left(\frac{5}{24} - \frac{1}{x}\right) = 5$

$\frac{5}{24} - \frac{1}{x} = \frac{1}{5}$

$\frac{1}{x} = \frac{5}{24} - \frac{1}{5}$

$\frac{1}{x} = \frac{25}{120} - \frac{24}{120}$

$\frac{1}{x} = \frac{1}{120}$

$x = 120$ hours

The leakage will take 120 hours to empty the full cistern.

2025: 19 May Shift 1

Pipe A can fill the tank 3 times faster than pipe B. If both pipes A and B running together can fill the tank in 15 minutes, then the time taken by B alone to fill the tank is:

2025: 22 May Shift 1

Pipe A can fill a tank in 24 hours and pipe B in 32 hours. If both the pipes are opened in an empty tank at the same time, then the time taken to fill the tank is:

2025: 21 May Shift 1

A pipe A can fill a tank in 4 hours. There are two outlet pipes, B and C, from the tank which can empty it in 8 and 10 hours respectively. If all the three pipes are opened simultaneously, how long will it take to fill the tank?

2025: 14 May Shift 2

Three pipes A, B and C can fill a tank in 12 hours, 15 hours and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, in how many hours will the tank be full?

2025: 27 May Shift 1

Two pipes can fill a tank in 6 minutes and 12 minutes respectively, and a third pipe can empty the tank at the rate of 18 liters per minute. If all the pipes working together can fill the empty tank in 5 minutes, the capacity of the tank is:

2025: 3 June Shift 1

Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. Both pipes A and B are opened together for some time and then pipe B is turned off. If the tank is filled in 15 minutes, then time for which the pipe B works is:

Two pipes can fill a cistern in 8 and 12 hours respectively. The pipes are opened simultaneously, and it takes 12 minutes more to fill the cistern due to leakage. If the cistern is full, what will be the time taken by the leakage to empty it?

Solution

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