# Pipes and Cisterns Quiz Set 005

### Question 1

A tap can fill a tank in 2 hours. Because of a leak it took \$2{3/8}\$ hours to fill the tank. When the tank has been completely filled, the tap is closed. How long will the water last in the tank?

A

\$12{2/3}\$ hrs.

B

\$20{1/2}\$ hrs.

C

\$11{2/3}\$ hrs.

D

\$9{2/5}\$ hrs.

Soln.
Ans: a

Work done by the leak in one hour is \$1/2 - 1/({19/8})\$ = \$1/2 - 8/19\$ = \$3/38\$. So the leak will complete the whole task in \${38/3}\$, which is same as: \$12{2/3}\$ hours.

### Question 2

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, 2 and 8 minutes. They are turned on at the same time. What is the ratio of blue ink after 3 minutes?

A

\${3/19}\$.

B

\$1{2/9}\$.

C

\${1/7}\$.

D

\$2{6/7}\$.

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}\$ = \${3/19}\$.

### Question 3

Pipe A can fill a cistern in 105 minutes, while the pipe B can fill it in 70 minutes. They are alternately open for 1 minute. How long will it take the cistern to fill completely?

A

84 mins.

B

85 mins.

C

83 mins.

D

86 mins.

Soln.
Ans: a

Let the total time taken be 2x minutes. Both X and Y run for x mins. So \$(x/70 + x/105)\$ = 1. Solving for x, we get x = 42, which gives 2x = 84.

### Question 4

One tap can fill a tank 4 times faster than the other. If they together fill it in 6 minutes, how much time does the slower alone take to fill the tank?

A

30 mins.

B

5 mins.

C

3 mins.

D

7 mins.

Soln.
Ans: a

Let the one minute work of the taps be 1/x and 4/x. We have \$1/x + 4/x = 1/6\$, which gives x = 5 × 6 = 30 mins.

### 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. 