Arithmetic

Time & Work

Medium

applied

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?

4.5 minutes

2.5 minutes

3.5 minutes

4 minutes

✅ Correct Option: 2

Pipe A fills the tank in 20 minutes, so its rate is $\dfrac{1}{20}$ of the tank per minute.

Pipe B fills the tank in 10 minutes, so its rate is $\dfrac{1}{10}$ of the tank per minute.

When both pipes work together, their combined rate is:

$\dfrac{1}{20} + \dfrac{1}{10}$

$= \dfrac{1}{20} + \dfrac{2}{20}$

$= \dfrac{3}{20}$ of the tank per minute

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

During these $t$ minutes, both pipes work together and fill:

$t \times \dfrac{3}{20}$ of the tank

After pipe B is turned off, pipe A works alone for $(15 - t)$ minutes and fills:

$(15 - t) \times \dfrac{1}{20}$ of the tank

The total work equals 1 full tank:

$t \times \dfrac{3}{20} + (15 - t) \times \dfrac{1}{20} = 1$

$\dfrac{3t}{20} + \dfrac{15 - t}{20} = 1$

$\dfrac{3t + 15 - t}{20} = 1$

$\dfrac{2t + 15}{20} = 1$

$2t + 15 = 20$

$2t = 5$

$t = 2.5$

Therefore, pipe B is turned off after 2.5 minutes.

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?

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?

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:

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?

2026: 29 May Shift 2

One pipe can fill a tank five times as fast as another pipe. If, together, two pipes can fill the tank in 30 minutes, how much time does the faster pipe alone take to fill the tank ?

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:

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?

Solution

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