Arithmetic

Time & Work

Medium

applied

Pipe A and B can fill a tank in 15 hours and 20 hours respectively. Pipe C can empty the tank in 25 hours. Pipes A, B and C works together but pipe C is closed after 10 hours , then time taken by pipe A and B to fill the remaining tank is:

12 hours

2 hours

8 hours

4 hours

✅ Correct Option: 2

Rate of Pipe A $= \dfrac{1}{15}$ tank per hour

Rate of Pipe B $= \dfrac{1}{20}$ tank per hour

Rate of Pipe C $= -\dfrac{1}{25}$ tank per hour (negative since it empties)

Combined rate when all three pipes work together:

$\dfrac{1}{15} + \dfrac{1}{20} - \dfrac{1}{25}$

Finding LCM of 15, 20, and 25 gives 300.

$\dfrac{20}{300} + \dfrac{15}{300} - \dfrac{12}{300}$

$= \dfrac{23}{300}$ tank per hour

Work done in first 10 hours with all three pipes:

$\dfrac{23}{300} \times 10$

$= \dfrac{230}{300}$

$= \dfrac{23}{30}$ of the tank

Remaining work for pipes A and B:

$1 - \dfrac{23}{30}$

$= \dfrac{7}{30}$ of the tank

Combined rate of pipes A and B only:

$\dfrac{1}{15} + \dfrac{1}{20}$

Finding LCM of 15 and 20 gives 60.

$\dfrac{4}{60} + \dfrac{3}{60}$

$= \dfrac{7}{60}$ tank per hour

Time taken by A and B to fill remaining tank:

$\text{Time} = \dfrac{\text{Work}}{\text{Rate}}$

$= \dfrac{7/30}{7/60}$

$= \dfrac{7}{30} \times \dfrac{60}{7}$

$= \dfrac{60}{30}$

$= 2$ hours

Therefore, pipes A and B take 2 hours to fill the remaining tank.

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: 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 ?

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?

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 :

2025: 16 May Shift 1

Pipe A can fill a tank three times faster than pipe B. If both pipes A and B are running together, they can fill the tank in 12 minutes, then the time taken by pipe B alone to fill the tank is:

2026: 18 May Shift 2

Two pipes can fill a tank in 12 and 15 minutes respectively and a waste pipe can empty 3.4 litres per minute. All the three pipes working together can fill the tank in 18 minutes. The capacity of the tank is

Pipe A and B can fill a tank in 15 hours and 20 hours respectively. Pipe C can empty the tank in 25 hours. Pipes A, B and C works together but pipe C is closed after 10 hours , then time taken by pipe A and B to fill the remaining tank is:

Solution

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