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 then pipe B is turned off. If the tank is filled in 15 minutes, then time for which the pipe B works is:

$15\frac{1}{2}$ minutes

$7\frac{1}{2}$ minutes

$8\frac{1}{2}$ minutes

$6\frac{1}{2}$ minutes

✅ Correct Option: 2

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

Pipe B fills the tank in 30 minutes, so its rate is $\frac{1}{30}$ tank per minute.

Let pipe B work for $t$ minutes.

Pipe A works for the entire 15 minutes.

Pipe B works for $t$ minutes, then is turned off.

Work done by Pipe A:

$\frac{1}{20} \times 15$

$= \frac{15}{20}$

$= \frac{3}{4}$ tank

Work done by Pipe B:

$\frac{1}{30} \times t$

$= \frac{t}{30}$ tank

Together they fill 1 complete tank:

$\frac{3}{4} + \frac{t}{30} = 1$

$\frac{t}{30} = 1 - \frac{3}{4}$

$\frac{t}{30} = \frac{1}{4}$

$t = \frac{30}{4}$

$t = 7.5$ minutes

$t = 7\frac{1}{2}$ minutes

Therefore, pipe B works for $7\frac{1}{2}$ minutes.

2026: 19 May Shift 2

Three pipes A, B and C can fill a tank together in 8 hours. After working at it together for 2 hours, B is closed and A and C can fill the remaining part in 9 hours. The time in which B alone can fill the tank is :

2025: 15 May Shift 2

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?

2026: 21 May Shift 2

A pipe can fill a tank with petrol in 3 hours. Due to leakage, it took $4\dfrac{2}{3}$ hours to fill the tank. How much time will it take for the leakage to drain all the petrol 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:

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 :

2024: 16 May Shift 1

Two pipes A and B together can fill a tank in $40$ minutes. Pipe A is twice as fast as pipe B. Pipe A alone can fill the tank in :

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:

Solution

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