# Pipes and Cisterns Quiz Set 010

### Question 1

Two pipes, A and B, can fill a cistern in 11 and 6 mins respectively. There is a leakage tap that can drain 12 liters of water per minute. If all three of them work together, the tank is filled in 6 minutes. What is the volume of the tank?

A

132 liters.

B

133 liters.

C

131 liters.

D

45 liters.

Soln.
Ans: a

Work done by the leakage in 1 min is \$1/11 + 1/6 - 1/6\$ = \${1/11}\$. This work is equivalent to a volume of 12 liters. So, the total volume is 12 × 11 = 132 liters.

### Question 2

Two taps X, Y and Z can fill a tank in 18, 15 and 11 minutes respectively. All the taps are turned on at the same time. After how many minutes is the tank completely filled?

A

\$4{146/211}\$ mins.

B

\$5{151/210}\$ mins.

C

\$3{140/213}\$ mins.

D

\$7{44/71}\$ mins.

Soln.
Ans: a

Let the time be x mins. Then sum of works done by X, Y and Z = 1. \$x/18 + x/15 + x/11 = 1\$. Solving, we get x = \$4{146/211}\$. Or use the shortcut \${abc}/{ab + bc + ca}\$. Another thing, instead of solving the entire calculation, you can keep an eye on the options to find the nearest answer.

### Question 3

Two taps X and Y can fill a tank in 6 and 9 minutes respectively. Both the taps are turned on at the same time. After how many minutes is the tank completely filled?

A

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

B

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

C

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

D

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

Soln.
Ans: a

Let the time be x mins. Then sum of works done by X and Y = 1. \$x/6 + x/9 = 1\$. Solving, we get x = \$3{3/5}\$.

### Question 4

Two pipes, A and B, can fill a cistern in 11 and 16 mins respectively. There is a leakage tap that can drain 9 liters of water per minute. If all three of them work together, the tank is filled in 17 minutes. What is the volume of the tank?

A

\$95{43/283}\$ liters.

B

\$96{139/282}\$ liters.

C

\$93{28/57}\$ liters.

D

\$97{44/95}\$ liters.

Soln.
Ans: a

Work done by the leakage in 1 min is \$1/11 + 1/16 - 1/17\$ = \${283/2992}\$. This work is equivalent to a volume of 9 liters. So, the total volume is 9 × \${2992/283}\$ = \${26928/283}\$, which is same as: \$95{43/283}\$ liters.

### Question 5

A tank is filled in 4 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

28 mins.

B

29 mins.

C

27 mins.

D

30 mins.

Soln.
Ans: a

Let the time taken by tap A be x mins. Then 4 minutes work of all the taps should add to 1. So we have, \$4 × 1/x + 4 × 2/x + 4 × 4/x\$ = 1, which is same as \$4 × 7/x\$ = 1. Solving, we get x = 28 mins. 