# Pipes and Cisterns Quiz Set 015

### Question 1

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 2

A tank is filled in 15 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

105 mins.

B

106 mins.

C

104 mins.

D

107 mins.

Soln.
Ans: a

Let the time taken by tap A be x mins. Then 15 minutes work of all the taps should add to 1. So we have, \$15 × 1/x + 15 × 2/x + 15 × 4/x\$ = 1, which is same as \$15 × 7/x\$ = 1. Solving, we get x = 105 mins.

### Question 3

Three taps R, G and B are supplying red, green and blue colored inks into a tub. They can independently fill the tub in 8, 8 and 5 minutes. They are turned on at the same time. What is the ratio of blue ink after 3 minutes?

A

\${4/9}\$.

B

\$1{5/8}\$.

C

\${4/11}\$.

D

\$2{9/11}\$.

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}\$ = \${4/9}\$.

### 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 3, 5 and 8 minutes. They are turned on at the same time. What is the ratio of blue ink after 3 minutes?

A

\${15/79}\$.

B

\$1{8/39}\$.

C

\${5/27}\$.

D

\$3{1/9}\$.

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}\$ = \${15/79}\$.

### Question 5

One tap can fill a tank 3 times faster than the other. If they together fill it in 14 minutes, how much time does the slower alone take to fill the tank?

A

56 mins.

B

4 mins.

C

2 mins.

D

6 mins.

Soln.
Ans: a

Let the one minute work of the taps be 1/x and 3/x. We have \$1/x + 3/x = 1/14\$, which gives x = 4 × 14 = 56 mins.