Arithmetic

Time & Work

Medium

applied

A tank has two outlet pipes, A and B, which together take 6 hours to empty a full tank when they are opened simultaneously. The tank was initially half-full and both the outlets were opened, after an hour an inlet pipe was also opened. If the inlet alone can fill the empty tank in 4 hours, how much time will it now take to fill the tank completely?

9 hrs

8 hrs

6 hrs

11 hrs

✅ Correct Option: 2

The tank capacity is 1 full tank.

Outlet pipes (A + B) combined empty the full tank in 6 hours.

Rate of outlets = $\frac{1}{6}$ tank per hour (emptying)

Inlet pipe fills the empty tank in 4 hours.

Rate of inlet = $\frac{1}{4}$ tank per hour (filling)

Initially the tank is half-full = $\frac{1}{2}$

Only outlets A and B work for the first hour.

Water emptied in 1 hour = $\frac{1}{6}$ of tank

Water remaining = $\frac{1}{2} - \frac{1}{6}$

$= \frac{3}{6} - \frac{1}{6}$

$= \frac{2}{6}$

$= \frac{1}{3}$

After 1 hour, the tank has $\frac{1}{3}$ water remaining.

After 1 hour, all three pipes work together.

Net rate = Inlet rate - Outlet rate

$= \frac{1}{4} - \frac{1}{6}$

$= \frac{3}{12} - \frac{2}{12}$

$= \frac{1}{12}$ tank per hour (filling)

Current water level = $\frac{1}{3}$

Target = $1$ (full tank)

Water needed = $1 - \frac{1}{3} = \frac{2}{3}$ of the tank

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

$= \frac{2/3}{1/12}$

$= \frac{2}{3} \times 12$

$= \frac{24}{3}$

$= 8$

Therefore, the tank will take 8 hours to fill completely after the inlet pipe is opened.

2026: 29 May Shift 1

Two pipes can fill a tank in 20 minutes and 24 minutes respectively, and a waste pipe can empty 3 gallons of water per minute. If all the three pipes working together can fill the tank in 15 minutes, then the capacity of the tank is :

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?

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

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?

2025: 13 May Shift 1

Three pipes A, B and C are installed to fill a tank. Pipes A and B opened together can fill the tank in the same time in which C can alone fill the tank. If pipe B can fill the tank 15 minutes faster than pipe A and 5 minutes slower than pipe C then the time required by pipe A to fill the tank alone is

2025: 29 May Shift 2

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

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)