# Pipes and Cisterns Quiz Set 013

### Question 1

Three taps R, G and B are supplying red, green and blue colored inks into a tub. They can independently fill the tub in 6, 8 and 6 minutes. They are turned on at the same time. What is the ratio of blue ink after 3 minutes?

A

\${4/11}\$.

B

\$1{1/2}\$.

C

\${4/13}\$.

D

\$2{11/13}\$.

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}\$ = \${4/11}\$.

### Question 2

A tank is (2/9)th filled with water. When 108 liters of water are added, it becomes (2/3)th filled. What is the capacity of the tank?

A

243 liters.

B

253 liters.

C

263 liters.

D

273 liters.

Soln.
Ans: a

Let x be the capacity in liters. \${2x}/9 + 108 = {2x}/3\$. Solving, x = 243 liters.

### Question 3

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 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

A city tanker is filled by two large pipes, X and Y, together in 18 and 12 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

9 mins.

B

10 mins.

C

8 mins.

D

11 mins.

Soln.
Ans: a

Let the time taken be x. Y is running for x mins, and X for x/2. So \$(x/12 + x/{2 × 18})\$ = 1. Solving for x, we get x = 9 mins.