# Pipes and Cisterns Quiz Set 020

### Question 1

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.

### Question 2

Two ink dispensers discharge ink into a color mixer. The first one can fill it in 22 minutes, whereas the second can fill it in 11 minutes. Both them are opened at the same time, but the second ink dispenser is turned off after 5 minutes. What is the total time required to fill the color mixer cistern?

A

12 mins.

B

13 mins.

C

11 mins.

D

14 mins.

Soln.
Ans: a

If the total time is T, the sum of works done by the ink dispensers are \$T/22 + 5/11\$ = 1. Solving, T = 12 mins.

### Question 3

Two ink dispensers discharge ink into a color mixer. The first one can fill it in 35 minutes, whereas the second can fill it in 7 minutes. Both them are opened at the same time, but the second ink dispenser is turned off after 4 minutes. What is the total time required to fill the color mixer cistern?

A

15 mins.

B

16 mins.

C

14 mins.

D

17 mins.

Soln.
Ans: a

If the total time is T, the sum of works done by the ink dispensers are \$T/35 + 4/7\$ = 1. Solving, T = 15 mins.

### Question 4

A tank is filled in 6 minutes by three taps running together. Times taken by the three taps independently are in an AP[Arithmetic Progression], whose first term is a and common difference d. Then, a and d satisfy the relation?

A

a3 - 18a2 - ad2 + 6d2 = 0.

B

a3 - 12a2 + ad2 + 6d2 = 0.

C

a3 - 6a2 - ad2 + 6d2 = 0.

D

a3 - 30a2 + ad2 + 6d2 = 0.

Soln.
Ans: a

Let the times taken by the three taps be a - d, a and a + d. Then 6 minutes work of all the taps should add to 1. So we have, \$6 × 1/{a - d} + 6 × 1/a + 6 × 1/{a + d}\$ = 1, which is same as a3 - 18a2 - ad2 + 6d2 = 0.

### Question 5

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.