# Pipes and Cisterns Quiz Set 001

### Question 1

Tap M can fill a cistern in 16 mins. And, a tap N can empty it in 11 mins. In how many minutes will the cistern be emptied if both the taps are opened together when the tank is \$7/15\$th already empty?

A

\$18{58/75}\$ mins.

B

\$20{3/74}\$ mins.

C

D

\$21{16/77}\$ mins.

Soln.
Ans: a

1 filled cistern can be emptied in \${16 × 11}/{16 - 11}\$ mins. So \$1 - 7/15\$ = \$8/15\$ filled cistern can be emptied in \${16 × 11}/{16 - 11}\$ × \$8/15\$ = \${1408/75}\$, which is same as: \$18{58/75}\$ mins.

### Question 2

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

A

20 mins.

B

21 mins.

C

19 mins.

D

22 mins.

Soln.
Ans: a

Let the time taken by the slower pipe alone be x. Then 4 × \$(1/x + 4/x)\$ = 1. Solving for x, we get x = 4 × 5 = 20 mins.

### Question 3

Two taps X, Y and Z can fill a tank in 18, 17 and 10 minutes respectively. All the taps are turned on at the same time. After how many minutes is the tank completely filled?

A

\$4{109/164}\$ mins.

B

\$5{114/163}\$ mins.

C

\$3{103/166}\$ mins.

D

\$7{95/166}\$ mins.

Soln.
Ans: a

Let the time be x mins. Then sum of works done by X, Y and Z = 1. \$x/18 + x/17 + x/10 = 1\$. Solving, we get x = \$4{109/164}\$. Or use the shortcut \${abc}/{ab + bc + ca}\$. Another thing, instead of solving the entire calculation, you can keep an eye on the options to find the nearest answer.

### Question 4

Tap X can fill the tank in 19 mins. Tap Y can empty it in 6 mins. In how many minutes will the tank be emptied if both the taps are opened together when the tank is \$13/17\$th full of water?

A

\$6{12/17}\$ mins.

B

\$8{3/16}\$ mins.

C

\$5{2/19}\$ mins.

D

\$8{13/19}\$ mins.

Soln.
Ans: a

1 filled tank can be emptied in \${19 × 6}/{19 - 6}\$ mins. So 13/17 can be emptied in \${19 × 6}/{19 - 6}\$ × \$13/17\$ = \${114/17}\$, which is same as: \$6{12/17}\$ mins.

### Question 5

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}\$.