Arithmetic

Time & Work

Medium

applied

A pipe A can fill a tank in 4 hours. There are two outlet pipes, B and C, from the tank which can empty it in 8 and 10 hours respectively. If all the three pipes are opened simultaneously, how long will it take to fill the tank?

30 hours

40 hours

45 hours

50 hours

✅ Correct Option: 2

Pipe A fills the tank in 4 hours.

Pipe B empties the tank in 8 hours.

Pipe C empties the tank in 10 hours.

When all three pipes are opened simultaneously, Pipe A adds water while Pipes B and C drain water out.

Each pipe's rate of work per hour:

Pipe A fills $\frac{1}{4}$ of the tank in 1 hour.

Pipe B empties $\frac{1}{8}$ of the tank in 1 hour.

Pipe C empties $\frac{1}{10}$ of the tank in 1 hour.

Net Rate = Filling Rate - Emptying Rate

Net Rate $= \frac{1}{4} - \frac{1}{8} - \frac{1}{10}$

The LCM of 4, 8, and 10 is 40.

$\frac{1}{4} = \frac{10}{40}$

$\frac{1}{8} = \frac{5}{40}$

$\frac{1}{10} = \frac{4}{40}$

Net Rate $= \frac{10}{40} - \frac{5}{40} - \frac{4}{40}$

Net Rate $= \frac{1}{40}$ of the tank per hour

If $\frac{1}{40}$ of the tank is filled in 1 hour, then the full tank will be filled in:

Time $= 1 \div \frac{1}{40}$

Time $= 40$ hours

Therefore, it will take 40 hours to fill the tank.

2026: 30 May Shift 2

Three pipes A, B, and C can fill a tank together in 2 hours. Pipes B and C take 3 hours to fill the tank, while pipes A and C take 4 hours to fill the tank. Which of the following statements are correct?

(A) Pipe A alone takes 6 hours to fill the tank.

(B) Pipe B alone takes 5 hours to fill the tank.

(D) Pipe C alone takes 12 hours to fill the tank.

Choose the correct answer from the options given below:

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

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?

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:

2025: 21 May Shift 2

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?

A pipe A can fill a tank in 4 hours. There are two outlet pipes, B and C, from the tank which can empty it in 8 and 10 hours respectively. If all the three pipes are opened simultaneously, how long will it take to fill the tank?

Solution

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