# Pipes and Cisterns Quiz Set 014

### Question 1

A tank is filled in \$1{1/3}\$ minutes by three taps running together. Times taken by the three taps to independently fill the tank are in an AP[Arithmetic Progression]. If the first tap is a leakage tap and the second tap takes 1 minute to fill the tank, then, the common difference of the AP can be?

A

3.

B

4.

C

2.

D

5.

Soln.
Ans: a

Let the times taken by the three taps be 1 - d, 1 and 1 + d. The time taken by the first tap will be negative because it is a leakage tap. Then \${4/3}\$ minutes work of all the taps should add to 1. So we have, \${4/3}\$ × \$(1/{1 - d} + 1/1 + 1/{1 + d})\$ = 1, which is same as \$2/{1 - d^2} + 1\$ = \${3/4}\$. Solving we get d = ±3.

### Question 2

A city tanker is filled by two large pipes, X and Y, together in 42 and 28 minutes respectively. On a certain day, pipe Y is used for first half of the time, and both X and Y are used for the second half. How many minutes does it take to fill the tank?

A

21 mins.

B

22 mins.

C

20 mins.

D

23 mins.

Soln.
Ans: a

Let the time taken be x. Y is running for x mins, and X for x/2. So \$(x/28 + x/{2 × 42})\$ = 1. Solving for x, we get x = 21 mins.

### Question 3

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 4

A bucket can be filled by a tap in 5 minutes. Another tap on the same bucket can empty it in 10 mins. How long will it take to fill the bucket if both the taps are opened together?

A

10 mins.

B

11 mins.

C

9 mins.

D

\$4{1/3}\$ mins.

Soln.
Ans: a

Net part filling in one hour is \$1/x - 1/y\$ = \$(y - x)/(xy)\$. So complete filling occurs in \$(xy)/(y - x)\$ = \${5 × 10}/{10 - 5}\$ = 10 mins.

### Question 5

What is the volume of the tank in liters if it measures 9m × 6m × 9m?

A

486000 liters.

B

486 liters.

C

3240 liters.

D

72900 liters.

Soln.
Ans: a

The volume in m3 is 9 × 6 × 9 = 486m3. But 1m3 = 1000L. So volume in liters = 486 × 1000 = 486000L.