# Pipes and Cisterns Quiz Set 017

### Question 1

Two pipes, A and B, can fill a bucket in 15 and 19 mins respectively. Both the pipes are opened simultaneously. The bucket is filled in 5 mins if B is turned off after how many minutes:

A

\$12{2/3}\$ mins.

B

\$20{1/2}\$ mins.

C

\$11{2/3}\$ mins.

D

\$9{2/5}\$ mins.

Soln.
Ans: a

Let B be closed after it has been filling for x minutes. Work done by pipes A and B should add to 1. So \$5/15\$ + \$x/19\$ = 1. Solving, we get x = \${38/3}\$, which is same as: \$12{2/3}\$.

### Question 2

A tap can fill a tank in 2 hours. Because of a leak it took \$2{2/7}\$ hours to fill the tank. When the tank has been completely filled, the tap is closed. How long will the water last in the tank?

A

16 hrs.

B

17 hrs.

C

15 hrs.

D

\$6{1/3}\$ hrs.

Soln.
Ans: a

Work done by the leak in one hour is \$1/2 - 1/({16/7})\$ = \$1/2 - 7/16\$ = \$2/32\$. So the leak will complete the whole task in 16 hours.

### Question 3

Two taps A and B can fill a tank in 15 and 30 minutes respectively. Both the taps are turned on at the same time. After how many minutes should B be turned off so that the tank can be filled in 13 minutes?

A

30 mins.

B

5 mins.

C

3 mins.

D

7 mins.

Soln.
Ans: a

Let B be closed after x mins. Then sum of works done by A and B = 1. \$13/15 + x/30 = 1\$. Solving, we get x = 4.

### Question 4

A tank is filled in 17 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 - 51a2 - ad2 + 17d2 = 0.

B

a3 - 34a2 + ad2 + 17d2 = 0.

C

a3 - 17a2 - ad2 + 17d2 = 0.

D

a3 - 85a2 + ad2 + 17d2 = 0.

Soln.
Ans: a

Let the times taken by the three taps be a - d, a and a + d. Then 17 minutes work of all the taps should add to 1. So we have, \$17 × 1/{a - d} + 17 × 1/a + 17 × 1/{a + d}\$ = 1, which is same as a3 - 51a2 - ad2 + 17d2 = 0.

### Question 5

What is the volume of the tank in liters if it measures 5m × 2m × 2m?

A

20000 liters.

B

20 liters.

C

200 liters.

D

5000 liters.

Soln.
Ans: a

The volume in m3 is 5 × 2 × 2 = 20m3. But 1m3 = 1000L. So volume in liters = 20 × 1000 = 20000L. 