Arithmetic

Time & Work

Medium

applied

Pipe A and B can fill a tank in 20 hours and 25 hours respectively, and pipe C can empty the full tank in 40 hours.If all the pipes are opened together, then how much time will be needed to make the tank full?

$15\frac{1}{13}$ hours

$15\frac{4}{13}$ hours

$15\frac{5}{13}$ hours

$15\frac{3}{13}$ hours

✅ Correct Option: 3

Pipe A fills the tank in 20 hours, Pipe B fills it in 25 hours, and Pipe C empties it in 40 hours.

Work done per hour by each pipe:

Pipe A $= \frac{1}{20}$

Pipe B $= \frac{1}{25}$

Pipe C $= \frac{1}{40}$

When all pipes are open together, the net rate per hour:

$\text{Net rate} = \frac{1}{20} + \frac{1}{25} - \frac{1}{40}$

Pipe C is subtracted because it removes water from the tank.

LCM of 20, 25, and 40:

$20 = 2^2 \times 5, \quad 25 = 5^2, \quad 40 = 2^3 \times 5$

$\text{LCM} = 2^3 \times 5^2 = 200$

Converting each fraction:

$\frac{1}{20} = \frac{10}{200}, \quad \frac{1}{25} = \frac{8}{200}, \quad \frac{1}{40} = \frac{5}{200}$

$\text{Net rate} = \frac{10}{200} + \frac{8}{200} - \frac{5}{200}$

$= \frac{13}{200} \text{ (tank per hour)}$

$\text{Time} = \frac{\text{Total Work}}{\text{Net Rate}}$

$= \frac{1}{\;\frac{13}{200}\;}$

$= \frac{200}{13}$

$= 15\frac{5}{13} \text{ hours}$

Therefore, the tank will be full in $\boxed{15\frac{5}{13} \text{ hours}}$ .

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:

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 :

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?

2025: 21 May Shift 1

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?

2026: 22 May Shift 2

A cistern can be filled by two pipes filling separately in 8 and 10 minutes respectively. Both the pipes are opened together but being clogged for a certain time, only $\frac{7}{10}$ of the full quantity of water flows through the former and only $\frac{3}{8}$ through the later pipe. The obstructions, however, being suddenly removed, the cistern is filled in 2 minutes from that moment. How long was it before the full flow began?

Pipe A and B can fill a tank in 20 hours and 25 hours respectively, and pipe C can empty the full tank in 40 hours.If all the pipes are opened together, then how much time will be needed to make the tank full?

Solution

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