Arithmetic

Time & Work

Medium

applied

Two pipes P and Q can fill a tank in 26 minutes and 52 minutes respectively. Both the pipes are opened together for some time and then pipe P is closed. If the tank is filled in 26 minutes, then after how many minutes pipe P is closed?

19 minutes

20 minutes

13 minutes

10 minutes

✅ Correct Option: 3

Pipe P fills the tank in 26 minutes.

In 1 minute, Pipe P fills $\frac{1}{26}$ of the tank.

Pipe Q fills the tank in 52 minutes.

In 1 minute, Pipe Q fills $\frac{1}{52}$ of the tank.

Let Pipe P be closed after $x$ minutes.

Both pipes work together for $x$ minutes.

Only Pipe Q works for the remaining $(26 - x)$ minutes.

Work done by both pipes in $x$ minutes:

$= x \times \left(\frac{1}{26} + \frac{1}{52}\right)$

$= x \times \left(\frac{2}{52} + \frac{1}{52}\right)$

$= x \times \frac{3}{52}$

$= \frac{3x}{52}$

Work done by Pipe Q alone in $(26 - x)$ minutes:

$= (26 - x) \times \frac{1}{52}$

$= \frac{26 - x}{52}$

Total work equals 1 full tank:

$\frac{3x}{52} + \frac{26 - x}{52} = 1$

$\frac{3x + 26 - x}{52} = 1$

$\frac{2x + 26}{52} = 1$

$2x + 26 = 52$

$2x = 26$

$x = 13$

Therefore, Pipe P should be closed after 13 minutes.

2025: 21 May Shift 2

Two pipes A and B can fill a tank in 20 minutes and 10 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 find after how many minutes pipe B is turned off?

2025: 13 May Shift 2

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?

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:

2026: 30 May Shift 1

A pump can fill a water tank in 4 hours but because of the leakage in the tank it took $4\frac{1}{4}$ hours to fill the tank. How much time will it take for the leakage to drain all the water of the full tank?

2026: 25 May Shift 1

Two pipes A and B can fill a tank in 10 minutes & 16 minutes respectively whereas a waste pipe can empty 3 litres per minute. All the three pipes working together can fill the tank in 8 minutes, then the capacity of the tank is:

2023: 15 June Shift 2

Two pipes A and B can fill a cistern in 15 minutes and 30 minutes respectively. Both pipes are opened together, but after 5 minute pipe B is turned off. The cistern will be full in total :

Two pipes P and Q can fill a tank in 26 minutes and 52 minutes respectively. Both the pipes are opened together for some time and then pipe P is closed. If the tank is filled in 26 minutes, then after how many minutes pipe P is closed?

Solution

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