# Pipes and Cisterns Quiz Set 007

### 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 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 2

Two pipes can together fill a cistern in 8 minutes. How long does the slower alone take if the speeds of the pipes are in the ratio 4 : 1?

A

40 mins.

B

41 mins.

C

39 mins.

D

42 mins.

Soln.
Ans: a

Let the time taken by the slower pipe alone be x. Then 8 × \$(1/x + 4/x)\$ = 1. Solving for x, we get x = 8 × 5 = 40 mins.

### Question 3

Tap X can fill the tank in 16 mins. Tap Y can empty it in 12 mins. In how many minutes will the tank be emptied if both the taps are opened together when the tank is \$9/18\$th full of water?

A

24 mins.

B

25 mins.

C

23 mins.

D

9 mins.

Soln.
Ans: a

1 filled tank can be emptied in \${16 × 12}/{16 - 12}\$ mins. So 9/18 can be emptied in \${16 × 12}/{16 - 12}\$ × \$9/18\$ = 24 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 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 5

Tap M can fill a cistern in 14 mins. And, a tap N can empty it in 12 mins. In how many minutes will the cistern be emptied if both the taps are opened together when the tank is \$5/19\$th already empty?

A

\$61{17/19}\$ mins.

B

\$66{7/18}\$ mins.

C

\$55{2/21}\$ mins.

D

\$58{5/7}\$ mins.

Soln.
Ans: a

1 filled cistern can be emptied in \${14 × 12}/{14 - 12}\$ mins. So \$1 - 5/19\$ = \$14/19\$ filled cistern can be emptied in \${14 × 12}/{14 - 12}\$ × \$14/19\$ = \${1176/19}\$, which is same as: \$61{17/19}\$ mins. 