# Pipes and Cisterns Quiz Set 018

### Question 1

Tap M can fill a cistern in 17 mins. And, a tap N can empty it in 15 mins. In how many minutes will the cistern be emptied if both the taps are opened together when the tank is \$11/14\$th already empty?

A

\$27{9/28}\$ mins.

B

\$29{10/27}\$ mins.

C

\$24{17/30}\$ mins.

D

\$28{3/10}\$ mins.

Soln.
Ans: a

1 filled cistern can be emptied in \${17 × 15}/{17 - 15}\$ mins. So \$1 - 11/14\$ = \$3/14\$ filled cistern can be emptied in \${17 × 15}/{17 - 15}\$ × \$3/14\$ = \${765/28}\$, which is same as: \$27{9/28}\$ mins.

### Question 2

A tank is (5/9)th filled with water. When 9 liters of water are added, it becomes (2/3)th filled. What is the capacity of the tank?

A

81 liters.

B

91 liters.

C

101 liters.

D

111 liters.

Soln.
Ans: a

Let x be the capacity in liters. \${5x}/9 + 9 = {2x}/3\$. Solving, x = 81 liters.

### Question 3

One tap can fill a tank 4 times faster than the other. If they together fill it in 7 minutes, how much time does the slower alone take to fill the tank?

A

35 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 = 1/7\$, which gives x = 5 × 7 = 35 mins.

### Question 4

A tank is filled in 16 minutes by three taps running together. Times taken by the three taps independently are in an AP[Arithmetic Progression], whose first term is a and common difference d. Then, a and d satisfy the relation?

A

a3 - 48a2 - ad2 + 16d2 = 0.

B

a3 - 32a2 + ad2 + 16d2 = 0.

C

a3 - 16a2 - ad2 + 16d2 = 0.

D

a3 - 80a2 + ad2 + 16d2 = 0.

Soln.
Ans: a

Let the times taken by the three taps be a - d, a and a + d. Then 16 minutes work of all the taps should add to 1. So we have, \$16 × 1/{a - d} + 16 × 1/a + 16 × 1/{a + d}\$ = 1, which is same as a3 - 48a2 - ad2 + 16d2 = 0.

### Question 5

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.