# Pipes and Cisterns Quiz Set 007

### Question 1

A bucket can be filled by a tap in 6 minutes. Another tap on the same bucket can empty it in 15 mins. How long will it take to fill the bucket if both the taps are opened together?

A

10 mins.

B

11 mins.

C

9 mins.

D

\$4{1/3}\$ mins.

Soln.
Ans: a

Net part filling in one hour is \$1/x - 1/y\$ = \$(y - x)/(xy)\$. So complete filling occurs in \$(xy)/(y - x)\$ = \${6 × 15}/{15 - 6}\$ = 10 mins.

### Question 2

A tap can fill a tank in 2 hours. Because of a leak it took \$2{2/7}\$ hours to fill the tank. When the tank has been completely filled, the tap is closed. How long will the water last in the tank?

A

16 hrs.

B

17 hrs.

C

15 hrs.

D

\$6{1/3}\$ hrs.

Soln.
Ans: a

Work done by the leak in one hour is \$1/2 - 1/({16/7})\$ = \$1/2 - 7/16\$ = \$2/32\$. So the leak will complete the whole task in 16 hours.

### Question 3

A tank is filled in 19 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

133 mins.

B

134 mins.

C

132 mins.

D

135 mins.

Soln.
Ans: a

Let the time taken by tap A be x mins. Then 19 minutes work of all the taps should add to 1. So we have, \$19 × 1/x + 19 × 2/x + 19 × 4/x\$ = 1, which is same as \$19 × 7/x\$ = 1. Solving, we get x = 133 mins.

### Question 4

What is the volume of the tank in liters if it measures 5m × 2m × 2m?

A

20000 liters.

B

20 liters.

C

200 liters.

D

5000 liters.

Soln.
Ans: a

The volume in m3 is 5 × 2 × 2 = 20m3. But 1m3 = 1000L. So volume in liters = 20 × 1000 = 20000L.

### Question 5

A city tanker is filled by two large pipes, X and Y, together in 42 and 28 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

21 mins.

B

22 mins.

C

20 mins.

D

23 mins.

Soln.
Ans: a

Let the time taken be x. Y is running for x mins, and X for x/2. So \$(x/28 + x/{2 × 42})\$ = 1. Solving for x, we get x = 21 mins.