Pipes and Cisterns Quiz Set 011

Question 1

Two taps A and B can fill a tank in 15 and 75 minutes respectively. Both the taps are turned on at the same time. After how many minutes should B be turned off so that the tank can be filled in 13 minutes?

A

10 mins.

B

11 mins.

C

9 mins.

D

13 mins.

Soln.
Ans: a

Let B be closed after x mins. Then sum of works done by A and B = 1. \$13/15 + x/75 = 1\$. Solving, we get x = 10.

Question 2

What is the volume of the tank in liters if it measures 3m × 5m × 4m?

A

60000 liters.

B

60 liters.

C

750 liters.

D

3600 liters.

Soln.
Ans: a

The volume in m3 is 3 × 5 × 4 = 60m3. But 1m3 = 1000L. So volume in liters = 60 × 1000 = 60000L.

Question 3

Tap X can fill the tank in 16 mins. Tap Y can empty it in 6 mins. In how many minutes will the tank be emptied if both the taps are opened together when the tank is \$6/16\$th full of water?

A

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

B

\$5{3/4}\$ mins.

C

\$1{6/7}\$ mins.

D

\$4{5/7}\$ mins.

Soln.
Ans: a

1 filled tank can be emptied in \${16 × 6}/{16 - 6}\$ mins. So 6/16 can be emptied in \${16 × 6}/{16 - 6}\$ × \$6/16\$ = \${18/5}\$, which is same as: \$3{3/5}\$ mins.

Question 4

A city tanker is filled by two large pipes, X and Y, together in 54 and 36 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

27 mins.

B

28 mins.

C

26 mins.

D

29 mins.

Soln.
Ans: a

Let the time taken be x. Y is running for x mins, and X for x/2. So \$(x/36 + x/{2 × 54})\$ = 1. Solving for x, we get x = 27 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. 