# Pipes and Cisterns Quiz Set 001

### Question 1

Two ink dispensers discharge ink into a color mixer. The first one can fill it in 36 minutes, whereas the second can fill it in 9 minutes. Both them are opened at the same time, but the second ink dispenser is turned off after 7 minutes. What is the total time required to fill the color mixer cistern?

A

8 mins.

B

9 mins.

C

7 mins.

D

10 mins.

Soln.
Ans: a

If the total time is T, the sum of works done by the ink dispensers are \$T/36 + 7/9\$ = 1. Solving, T = 8 mins.

### Question 2

Two taps X and Y can fill a tank in 9 and 4 minutes respectively. Both the taps are turned on at the same time. After how many minutes is the tank completely filled?

A

\$2{10/13}\$ mins.

B

\$4{1/12}\$ mins.

C

\$1{8/15}\$ mins.

D

5 mins.

Soln.
Ans: a

Let the time be x mins. Then sum of works done by X and Y = 1. \$x/9 + x/4 = 1\$. Solving, we get x = \$2{10/13}\$.

### Question 3

A tank is filled in 15 minutes by three taps running together. Tap A is twice as fast as tap B, and tap B is twice as fast as tap C. How much time will tap A take to fill the tank?

A

105 mins.

B

106 mins.

C

104 mins.

D

107 mins.

Soln.
Ans: a

Let the time taken by tap A be x mins. Then 15 minutes work of all the taps should add to 1. So we have, \$15 × 1/x + 15 × 2/x + 15 × 4/x\$ = 1, which is same as \$15 × 7/x\$ = 1. Solving, we get x = 105 mins.

### Question 4

One tap can fill a tank 4 times faster than the other. If they together fill it in 5 minutes, how much time does the slower alone take to fill the tank?

A

25 mins.

B

5 mins.

C

3 mins.

D

7 mins.

Soln.
Ans: a

Let the one minute work of the taps be 1/x and 4/x. We have \$1/x + 4/x = 1/5\$, which gives x = 5 × 5 = 25 mins.

### Question 5

Two ink dispensers discharge ink into a color mixer. The first one can fill it in 40 minutes, whereas the second can fill it in 10 minutes. Both them are opened at the same time, but the second ink dispenser is turned off after 5 minutes. What is the total time required to fill the color mixer cistern?

A

20 mins.

B

21 mins.

C

19 mins.

D

22 mins.

Soln.
Ans: a

If the total time is T, the sum of works done by the ink dispensers are \$T/40 + 5/10\$ = 1. Solving, T = 20 mins.