# Pipes and Cisterns Quiz Set 004

### Question 1

What is the volume of the tank in liters if it measures 5m × 9m × 8m?

A

360000 liters.

B

360 liters.

C

4050 liters.

D

20000 liters.

Soln.
Ans: a

The volume in m3 is 5 × 9 × 8 = 360m3. But 1m3 = 1000L. So volume in liters = 360 × 1000 = 360000L.

### Question 2

A city tanker is filled by two large pipes, X and Y, together in 18 and 12 minutes respectively. On a certain day, pipe Y is used for first half of the time, and both X and Y are used for the second half. How many minutes does it take to fill the tank?

A

9 mins.

B

10 mins.

C

8 mins.

D

11 mins.

Soln.
Ans: a

Let the time taken be x. Y is running for x mins, and X for x/2. So \$(x/12 + x/{2 × 18})\$ = 1. Solving for x, we get x = 9 mins.

### Question 3

Two pipes can together fill a cistern in 3 minutes. How long does the slower alone take if the speeds of the pipes are in the ratio 4 : 1?

A

15 mins.

B

16 mins.

C

14 mins.

D

17 mins.

Soln.
Ans: a

Let the time taken by the slower pipe alone be x. Then 3 × \$(1/x + 4/x)\$ = 1. Solving for x, we get x = 3 × 5 = 15 mins.

### Question 4

A tank is filled in \$1{1/11}\$ minutes by three taps running together. Times taken by the three taps to independently fill the tank are in an AP[Arithmetic Progression]. If the first tap is a leakage tap and the second tap takes 1 minute to fill the tank, then, the common difference of the AP can be?

A

5.

B

6.

C

4.

D

7.

Soln.
Ans: a

Let the times taken by the three taps be 1 - d, 1 and 1 + d. The time taken by the first tap will be negative because it is a leakage tap. Then \${12/11}\$ minutes work of all the taps should add to 1. So we have, \${12/11}\$ × \$(1/{1 - d} + 1/1 + 1/{1 + d})\$ = 1, which is same as \$2/{1 - d^2} + 1\$ = \${11/12}\$. Solving we get d = ±5.

### Question 5

Three taps R, G and B are supplying red, green and blue colored inks into a tub. They can independently fill the tub in 6, 8 and 6 minutes. They are turned on at the same time. What is the ratio of blue ink after 3 minutes?

A

\${4/11}\$.

B

\$1{1/2}\$.

C

\${4/13}\$.

D

\$2{11/13}\$.

Soln.
Ans: a

Let the time taken by them to independently fill the tank be r, g and b minutes. Ink discharged by the blue tap is \$3/b\$. The total of all the inks is \$3/r + 3/g + 3/b\$. The ratio is \${1/b}/{1/r + 1/g + 1/b}\$, which simplifies to \${rg}/{rg + gb + br}\$ = \${4/11}\$.