Arithmetic

Time & Work

Medium

applied

Two pipes A and B can fill a tank respectively in 30 min and 45 min. Both A and B are opened together for some time and then pipe B is turned off. If the tank is filled in 20 min, then find after how many minutes the pipe B is turned off?

5 min

30 min

15 min

25 min

✅ Correct Option: 3

Pipe A fills the tank in 30 minutes.

Pipe B fills the tank in 45 minutes.

Both pipes are opened together, then pipe B is turned off after some time.

The tank is filled in 20 minutes total.

Pipe A's rate $= \dfrac{1}{30}$ tank per minute

Pipe B's rate $= \dfrac{1}{45}$ tank per minute

Combined rate when both work together:

$\dfrac{1}{30} + \dfrac{1}{45}$

$= \dfrac{3}{90} + \dfrac{2}{90}$

$= \dfrac{5}{90}$

$= \dfrac{1}{18}$ tank per minute

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

During the first $t$ minutes, both pipes work together.

During the remaining $(20 - t)$ minutes, only pipe A works.

Work done by both pipes together $= t \times \dfrac{1}{18} = \dfrac{t}{18}$

Work done by pipe A alone $= (20 - t) \times \dfrac{1}{30} = \dfrac{20 - t}{30}$

Total work done equals 1 full tank:

$\dfrac{t}{18} + \dfrac{20 - t}{30} = 1$

Multiplying by 90:

$5t + 3(20 - t) = 90$

$5t + 60 - 3t = 90$

$2t + 60 = 90$

$2t = 30$

$t = 15$

Pipe B is turned off after 15 minutes.

2026: 22 May Shift 1

A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe ,then the time required by the first pipe to fill the tank alone is :

2026: 12 May Shift 2

Match List-I with List-II

List-I	List-II
(A) If an inlet pipe can fill a tank in $x$ hours, but due to a leakage in the bottom it is filled in $y$ hours, then time (in hours) taken to empty the tank due to leakage	(I) $\dfrac{yz+zx-xy}{xyz}$
(B) If two inlet pipes take $x$ & $y$ hours respectively to fill the tank and the third outlet pipe takes $z$ hours to empty the tank. If all three of them are opened together, then the net part of the tank filled in 1 hour	(II) $\dfrac{1}{x}$
(C) If a pipe can fill the tank completely in $x$ hours, then the part of the tank filled in 1 hour	(III) $\dfrac{xy}{y-x}$
(D) If two inlet pipes can fill a tank in $x$ & $y$ hours. If both pipes are opened at the same time, then net part of the tank filled in 1 hour	(IV) $\dfrac{x+y}{xy}$

Choose the correct answer from the options given below:

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 :

2026: 31 May Shift 2

A tap can fill a tank in 45 minutes whereas another tap can empty it in 1 hour 30 minutes. If both taps are opened at 9 A.M., then the time at which the tank will be filled is

2026: 19 May Shift 1

Three taps A, B and C can fill a tank in 12 minutes, 15 minutes and 20 minutes respectively. If tap A is opened all the time while tap B and C are opened for 1 minute each alternately such that tap B opened first, then the time taken to fill the tank is :

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?

Two pipes A and B can fill a tank respectively in 30 min and 45 min. Both A and B are opened together for some time and then pipe B is turned off. If the tank is filled in 20 min, then find after how many minutes the pipe B is turned off?

Solution

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