# Pipes and Cisterns Quiz Set 002

### Question 1

Two taps X and Y can fill a tank in 7 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{15/16}\$ mins.

B

\$5{4/15}\$ mins.

C

\$2{11/18}\$ mins.

D

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

Soln.
Ans: a

Let the time be x mins. Then sum of works done by X and Y = 1. \$x/7 + x/9 = 1\$. Solving, we get x = \$3{15/16}\$.

### Question 2

A tank is (2/9)th filled with water. When 64 liters of water are added, it becomes (2/5)th filled. What is the capacity of the tank?

A

360 liters.

B

370 liters.

C

380 liters.

D

390 liters.

Soln.
Ans: a

Let x be the capacity in liters. \${2x}/9 + 64 = {2x}/5\$. Solving, x = 360 liters.

### Question 3

Two taps X and Y can fill a tank in 4 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{1/17}\$ mins.

B

\$4{5/16}\$ mins.

C

\$1{16/19}\$ mins.

D

\$5{8/19}\$ mins.

Soln.
Ans: a

Let the time be x mins. Then sum of works done by X and Y = 1. \$x/4 + x/13 = 1\$. Solving, we get x = \$3{1/17}\$.

### Question 4

Two taps X, Y and Z can fill a tank in 4, 16 and 6 minutes respectively. All the taps are turned on at the same time. After how many minutes is the tank completely filled?

A

\$2{2/23}\$ mins.

B

\$3{5/22}\$ mins.

C

1 mins.

D

\$4{17/25}\$ mins.

Soln.
Ans: a

Let the time be x mins. Then sum of works done by X, Y and Z = 1. \$x/4 + x/16 + x/6 = 1\$. Solving, we get x = \$2{2/23}\$. 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 5

Two taps A and B can fill a tank in 16 and 32 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 12 minutes?

A

8 mins.

B

9 mins.

C

7 mins.

D

11 mins.

Soln.
Ans: a

Let B be closed after x mins. Then sum of works done by A and B = 1. \$12/16 + x/32 = 1\$. Solving, we get x = 8. 