## Pipes and Cisterns Solved Problems & Solutions with Explanation

## Pipes and Cisterns

A pipe is connected to a tank or cistern which will be used to fill or empty the tank. Accordingly, it is known as an inlet or an outlet. Problems on pipes and cisterns are similar to problems on time and work.

**Inlet:**A pipe connected to fill a tank is known as an inlet.**Outlet:**A pipe connected to empty a tank is known as an outlet.

### Formulas of Pipes and Cisterns

- If an inlet connected to a tank fills it in X hours, part of the tank filled in one hour is = 1/X
- If an outlet connected to a tank empties it in Y hours, part of the tank emptied in one hour is = 1/Y
- An inlet can fill a tank in X hours and an outlet can empty the same tank in Y hours. If both the pipes are opened at the same time and Y > X, the net part of the tank filled in one hour is given by = (1 / X) – (1 / Y).
- If a pipe can fill a tank in X hours and another pipe can empty the full tank in Y hours, then on opening both the pipes, the remaining part emptied in 1 hour = (1 / Y) – (1 / X).

### Pipes and Cisterns Problems With Solutions

**1. In 2 hours a pump can fill up a tank with water. It took 2 1/3 hours to fill the tank, because of a leak. The leak can drain all tank water into:**

- A. 4 1/3 hours
- B. 7 hours
- C. 8 hours
- D. 14 hours

**Answer:** Option D (14 hours)

**2. A tank is filled with 3 uniform flow pipes. The first two pipes operating at the same time fill the tank while the third pipe fills the tank alone. The second pipe fills the tank fifteen hours faster than the first pipe, and four hours faster than the third. The time required to fill the tank by the first pipe is**

- A. 6 hours
- B. 15 hours
- C. 10 hours
- D. 30 hours

**Answer:** Option B (15 hours)

**3. Two A and B pipes will fill a tank in 2 minutes and 15 minutes respectively, separately. Both pipes are opened together but the pipe A is switched off 4 minutes after launch. How long does it take to fill your tank?**

- A. 9 min
- B. 10 min
- C. 11 min
- D. 12 min

**Answer:** Option B (10 min)

**4. A cistern has a leak that in 20 minutes would empty the cistern out. A tap that admits 4 liters per minute into the cistern is turned on and drained in 24 minutes. How many liters does the cistern carry?**

- A. 480 liters
- B. 600 liters
- C. 720 liters
- D. 800 liters

**Answer:** Option A (480 liters)

**5. In 12 and 15 minutes respectively two pipes A and B will fill a cistern. Both are opened together but A is turned off after 3 minutes. How much longer will the cistern be filled up after?**

- A. 3 1/4 min
- B. 5 1/4 min
- C. 8 1/4 min
- D. 9 1/4 min

**Answer:** Option C (8 1/4 min)

**6. Two pipes A and B, in 15 minutes and 40 minutes respectively, can fill a tank. Both pipes open together but pipe A is shut off after 4 minutes. What is the total time required to fill the tank?**

- A. 20 min 10 sec
- B. 25 min 20 sec
- C. 10 min 10 sec
- D. 29 min 20 sec

**Answer:** Option D (29 min 20 sec)

**7. Within 25 and 30 minutes respectively two pipes can fill a tank and a waste pipe can drain 3 gallons per minute. The tank can be filled in in 15 minutes with all three pipes working together. The tank capacity is:**

- A. 250 gallons
- B. 450 gallons
- C. 150 gallons
- D. 120 gallons

**Answer:** Option B (450 gallons)

**8. In 18 minutes and 15 minutes, two pipes can fill one tank. The tank can be emptied in 45 minutes by an exit pipe. If when the tank is empty all the pipes are opened, then how many minutes will it take to fill the tank?**

- A. 12
- B. 13
- C. 11
- D. 10

**Answer:** Option D (10)

**9. A cistern can be filled in within 3 hours by a tap, while another tap can empty it in 8 hours. If both taps are opened at the same time, then how long will the cistern be filled after?**

- A. 1.8 hr
- B. 3.6 hr
- C. 4.8 hr
- D. 2.4 hr

**Answer:** Option C (4.8 hr)

**10. Bucket P has a power of three times that of bucket Q. Bucket P needs 80 turns to fill in the empty tank. How many turns will it take for both P and Q buckets, each turn filling the empty drum together?**

- A. 60
- B. 30
- C. 45
- D. 80

**Answer:** Option A (60)