Arithmetic

Time & Work

Medium

applied

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 pipe B is turned off. If the tank is filled in 15 minutes, then after how many minutes pipe B is turned off?

5 minutes

8 minutes

12 minutes

7.5 minutes

✅ Correct Option: 4

Pipe A fills the tank in 20 minutes, so in 1 minute, Pipe A fills $\frac{1}{20}$ of the tank.

Pipe B fills the tank in 30 minutes, so in 1 minute, Pipe B fills $\frac{1}{30}$ of the tank.

When both pipes work together, they fill per minute:

$\frac{1}{20} + \frac{1}{30}$

$= \frac{3}{60} + \frac{2}{60}$

$= \frac{5}{60}$

$= \frac{1}{12}$ of the tank

Let Pipe B work for $t$ minutes before being turned off.

Work done when both pipes operate (for $t$ minutes):

$= t \times \frac{1}{12} = \frac{t}{12}$

Work done when only Pipe A operates (for remaining time):

Remaining time $= 15 - t$ minutes

$= (15 - t) \times \frac{1}{20} = \frac{15 - t}{20}$

Total work equals 1 full tank:

$\frac{t}{12} + \frac{15 - t}{20} = 1$

Multiplying by 60:

$5t + 3(15 - t) = 60$

$5t + 45 - 3t = 60$

$2t = 15$

$t = 7.5$

Therefore, Pipe B is turned off after 7.5 minutes.

2025: 2 June Shift 1

Three pipes A, B & C fill a tank in 3 hours working simultaneously. The pipe C is twice as faster as B and B is twice as fast as A. The time taken by pipe A alone to fill the tank is:

2026: 15 May Shift 1

Three pipes A, B, and C can fill a tank together in 10 hours. After working at it together for 2 hours, B is closed and A and C can fill the remaining part in 12 hours. The time in which B alone can fill the tank is

2025: 26 May Shift 2

Inlet Pipe A can fill a tank in 30 minutes, and outlet pipes B and C can empty the tank in 2 hours each. If all 3 pipes operate together, the tank will be filled in:

2026: 26 May Shift 2

Two pipes A and B fill a tank in 12 minutes and 15 minutes respectively. If both the pipes are opened simultaneously and pipe A is closed after 3 minutes, then how much more time will it take to fill the tank with pipe B?

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: 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?

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 pipe B is turned off. If the tank is filled in 15 minutes, then after how many minutes pipe B is turned off?

Solution

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