some terminology for pipe and cistern –

- An inlet pipe fill the tank/cistern.
- An outlet pipe or waste pipe empties a cistern.
- Time – Stands for time taken for filling or emptying.
- When a cistern is filled completely, then amount of work done (filling) = 1

**Let’s move on some basic concept for Pipes and Cistern Short Tricks :**

### Concept 1. –

If an inlet pipe can fill a cistern in ‘x’ hours, then

### Concept 2. –

If an outlet pipe can empty a cistern in ‘y’ hours, then

### Concept 3. –

Net work done in 1 hours = (filling work in 1 hour) – (Empty work in 1 hour)

If W is ( – ) ve, then cistern is emptied.

### Concept 4. –

### Concept 5. –

If more than one inlet pipe or more than one out let pipes are fitted, then

Time taken to fill or Empty = 1/part filled or emptied in 1 hour

### Concept 6. –

If one inlet pipe can fill in t1 hours and one outlet pipe can empties it in t2 hours, then part of cistern filled or emptied in 1 hours = (1/t1 – 1/t2)

Note : Chain rule will work here same as Time and Work problem.

**Problem on Leakage:**

Two fill pipes can separately fill a cistern, say, in ‘x’ hours and ‘y’ hours respectively, but due to leak it takes ‘P’ hours extra to fill the cistern. Now both pipes are closed and the fill cistern can be emptied through the leak in ‘T’ hours,

If there is only one fill pipe, then above relation can be reduces to

Empty time by leak, T

### Pipes and Cistern – Sample Questions

It is suggested that candidates must solve more and more questions to be able to understand the concept better and also to answer the questions quickly and efficiently.

Given below are a few sample questions for the reference of candidates.

**Q 1.** It takes 6 hours for three pipes, X, Y and Z to fill a tank. When the three worked together for 2 hours, Z was closed and, X and Y filled the remaining tank in 7 hours. How many hours would it take Z alone to fill the tank?

- 15 hours
- 23 hours
- 12 hours
- 14 hours
- 21 hours

**Answer: (4) 14 hours**

**Solution:**

Part of the tank which was filled in 2 hours = 2/6 = ⅓

The part of the tank remaining to be filled = 1 – ⅓ = ⅔

Work done by X and Y together in 7 hours = ⅔

Work done by X and Y together in 1 hour = [(⅔) / 7] = 2/21

Work done by Z in 1 hour = [{(X+Y+X)’s 1 hour’s work } – {(X+Y)’s 1 hour’s work}]

= (⅙) – (2/21) = 1/14

Therefore, it would take Z alone 14 hours to fill in the tank

**Q 2. **It takes two pipes A and B, running together, to fill a tank in 6 minutes. It takes A 5 minutes less than B to fill the tank, then what will be the time taken by B alone to fill the tank?

- 10 minutes
- 15 minutes
- 20 minutes
- 25 minutes
- 8 minutes

**Answer: (2) 15 minutes**

**Solution:**

Let the time taken by pipe A to fill the tank be x minutes

Time is taken by pipe B to fill the tank = x+5 minutes

So, 1/x + 1/(x+5) = 1/6

⇒ x = 10

Thus, time taken by B alone to fill the tank is 10+5, i.e., 15 minutes

**Q 3. **If two pipes can fill a tank in 24 and 20 minutes respectively and another pipe can empty 3 gallons of water per minute from that tank. When all the three pipes are working together, it takes 15 minutes to fill the tank. What is the capacity of the tank?

- 100 gallons
- 150 gallons
- 125 gallons
- 130 gallons
- 120 gallons

**Answer: (5) 120 gallons**

**Solution:**

Work done by the outlet pipe in 1 minute = {1/15 – (1/24)+(1/20)} = 1/15 – 11/120 = -(1/40)

Here, the negative sign indicates the negative work done, that is the loss of water from the outlet

The capacity of 1/40 part = 3 gallons

So, Capacity of whole tank = 40×3 = 120 gallons

**Q 4.** It takes 20 minutes for pipe A to fill the tank completely and it takes 30 minutes for pipe B to fill the tank completely. If both the inlets are opened together, then how much time will be taken to fill the tank completely?

- 15 minutes
- 12 minutes
- 11 minutes
- 10 minutes
- 22 minutes

**Answer: (2) 12 minutes**

**Solution:**

A portion of the tank filled by pipe A in 1 minute = 1/20

A portion of the tank filled by pipe B in 1 minute = 1/30

Total portion filled by both pipe A and B in 1 minute = (1/20 + 1/30) = 1/12

Thus it will take 12 minutes to fill the tank completely if both the inlets are opened together.

**Q 5. **Pipe A can fill the tank 3 times faster in comparison to pipe B. It takes 36 minutes for pipe A and B to fill the tank together. How much time will pipe B alone take to fill the tank?

- 100 minutes
- 124 minutes
- 134 minutes
- 144 minutes
- 154 minutes

**Answer: (4) 144 minutes**

**Solution:**

Let the time taken by pipe B be x minutes

So, the time taken by pipe A = x/3 minutes

Thus, 1/3 + 3/x = 1/36

⇒ 4/x = 1/36

⇒ x = 4×36

⇒ x = 144 minutes