# Pipes and Cisterns Quiz Set 008

### Question 1

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

A

405000 liters.

B

405 liters.

C

2250 liters.

D

72900 liters.

Soln.
Ans: a

The volume in m3 is 9 × 5 × 9 = 405m3. But 1m3 = 1000L. So volume in liters = 405 × 1000 = 405000L.

### Question 2

Tap M can fill a cistern in 12 mins. And, a tap N can empty it in 7 mins. In how many minutes will the cistern be emptied if both the taps are opened together when the tank is \$6/13\$th already empty?

A

\$9{3/65}\$ mins.

B

\$10{13/64}\$ mins.

C

\$7{54/67}\$ mins.

D

\$11{46/67}\$ mins.

Soln.
Ans: a

1 filled cistern can be emptied in \${12 × 7}/{12 - 7}\$ mins. So \$1 - 6/13\$ = \$7/13\$ filled cistern can be emptied in \${12 × 7}/{12 - 7}\$ × \$7/13\$ = \${588/65}\$, which is same as: \$9{3/65}\$ mins.

### Question 3

One tap can fill a tank 3 times faster than the other. If they together fill it in 14 minutes, how much time does the slower alone take to fill the tank?

A

56 mins.

B

4 mins.

C

2 mins.

D

6 mins.

Soln.
Ans: a

Let the one minute work of the taps be 1/x and 3/x. We have \$1/x + 3/x = 1/14\$, which gives x = 4 × 14 = 56 mins.

### Question 4

Two taps X and Y can fill a tank in 5 and 13 minutes respectively. Both the taps are turned on at the same time. After how many minutes is the tank completely filled?

A

\$3{11/18}\$ mins.

B

\$4{15/17}\$ mins.

C

\$2{7/20}\$ mins.

D

\$5{19/20}\$ mins.

Soln.
Ans: a

Let the time be x mins. Then sum of works done by X and Y = 1. \$x/5 + x/13 = 1\$. Solving, we get x = \$3{11/18}\$.

### Question 5

Pipe A can fill a cistern in 45 minutes, while the pipe B can fill it in 30 minutes. They are alternately open for 1 minute. How long will it take the cistern to fill completely?

A

36 mins.

B

37 mins.

C

35 mins.

D

38 mins.

Soln.
Ans: a

Let the total time taken be 2x minutes. Both X and Y run for x mins. So \$(x/30 + x/45)\$ = 1. Solving for x, we get x = 18, which gives 2x = 36. 