# Pipes and Cisterns Quiz Set 016

### Question 1

A city tanker is filled by two large pipes, X and Y, together in 24 and 16 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

12 mins.

B

13 mins.

C

11 mins.

D

14 mins.

Soln.
Ans: a

Let the time taken be x. Y is running for x mins, and X for x/2. So \$(x/16 + x/{2 × 24})\$ = 1. Solving for x, we get x = 12 mins.

### Question 2

Pipe A can fill a cistern in 60 minutes, while the pipe B can fill it in 40 minutes. They are alternately open for 1 minute. How long will it take the cistern to fill completely?

A

48 mins.

B

49 mins.

C

47 mins.

D

50 mins.

Soln.
Ans: a

Let the total time taken be 2x minutes. Both X and Y run for x mins. So \$(x/40 + x/60)\$ = 1. Solving for x, we get x = 24, which gives 2x = 48.

### Question 3

Two ink dispensers discharge ink into a color mixer. The first one can fill it in 21 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

9 mins.

B

10 mins.

C

8 mins.

D

11 mins.

Soln.
Ans: a

If the total time is T, the sum of works done by the ink dispensers are \$T/21 + 4/7\$ = 1. Solving, T = 9 mins.

### Question 4

Three taps R, G and B are supplying red, green and blue colored inks into a tub. They can independently fill the tub in 7, 3 and 6 minutes. They are turned on at the same time. What is the ratio of blue ink after 3 minutes?

A

\${7/27}\$.

B

\$1{4/13}\$.

C

\${7/29}\$.

D

\$3{1/29}\$.

Soln.
Ans: a

Let the time taken by them to independently fill the tank be r, g and b minutes. Ink discharged by the blue tap is \$3/b\$. The total of all the inks is \$3/r + 3/g + 3/b\$. The ratio is \${1/b}/{1/r + 1/g + 1/b}\$, which simplifies to \${rg}/{rg + gb + br}\$ = \${7/27}\$.

### Question 5

A tank is (3/8)th filled with water. When 68 liters of water are added, it becomes (4/5)th filled. What is the capacity of the tank?

A

160 liters.

B

170 liters.

C

180 liters.

D

190 liters.

Soln.
Ans: a

Let x be the capacity in liters. \${3x}/8 + 68 = {4x}/5\$. Solving, x = 160 liters. 