# Pipes and Cisterns Quiz Set 002

### Question 1

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 2

Two pipes, A and B, can fill a bucket in 19 and 5 mins respectively. Both the pipes are opened simultaneously. The bucket is filled in 11 mins if B is turned off after how many minutes:

A

\$2{2/19}\$ mins.

B

\$3{5/18}\$ mins.

C

1 mins.

D

\$4{13/21}\$ mins.

Soln.
Ans: a

Let B be closed after it has been filling for x minutes. Work done by pipes A and B should add to 1. So \$11/19\$ + \$x/5\$ = 1. Solving, we get x = \${40/19}\$, which is same as: \$2{2/19}\$.

### Question 3

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.

### Question 4

Two ink dispensers discharge ink into a color mixer. The first one can fill it in 21 minutes, whereas the second can fill it in 7 minutes. Both them are opened at the same time, but the second ink dispenser is turned off after 4 minutes. What is the total time required to fill the color mixer cistern?

A

9 mins.

B

10 mins.

C

8 mins.

D

11 mins.

Soln.
Ans: a

If the total time is T, the sum of works done by the ink dispensers are \$T/21 + 4/7\$ = 1. Solving, T = 9 mins.

### Question 5

A tank is filled in 9 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

63 mins.

B

64 mins.

C

62 mins.

D

65 mins.

Soln.
Ans: a

Let the time taken by tap A be x mins. Then 9 minutes work of all the taps should add to 1. So we have, \$9 × 1/x + 9 × 2/x + 9 × 4/x\$ = 1, which is same as \$9 × 7/x\$ = 1. Solving, we get x = 63 mins.