# Pipes and Cisterns Quiz Set 016

### Question 1

Two taps X and Y can fill a tank in 7 and 9 minutes respectively. Both the taps are turned on at the same time. After how many minutes is the tank completely filled?

A

\$3{15/16}\$ mins.

B

\$5{4/15}\$ mins.

C

\$2{11/18}\$ mins.

D

\$6{1/6}\$ mins.

Soln.
Ans: a

Let the time be x mins. Then sum of works done by X and Y = 1. \$x/7 + x/9 = 1\$. Solving, we get x = \$3{15/16}\$.

### Question 2

A tap can fill a tank in 2 hours. Because of a leak it took \$3{1/6}\$ 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

\$5{3/7}\$ hrs.

B

\$7{1/2}\$ hrs.

C

\$3{4/9}\$ hrs.

D

\$6{5/9}\$ hrs.

Soln.
Ans: a

Work done by the leak in one hour is \$1/2 - 1/({19/6})\$ = \$1/2 - 6/19\$ = \$7/38\$. So the leak will complete the whole task in \${38/7}\$, which is same as: \$5{3/7}\$ hours.

### Question 3

A bucket can be filled by a tap in 8 minutes. Another tap on the same bucket can empty it in 12 mins. How long will it take to fill the bucket if both the taps are opened together?

A

24 mins.

B

25 mins.

C

23 mins.

D

9 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)\$ = \${8 × 12}/{12 - 8}\$ = 24 mins.

### Question 4

Two taps A and B can fill a tank in 16 and 32 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 12 minutes?

A

8 mins.

B

9 mins.

C

7 mins.

D

11 mins.

Soln.
Ans: a

Let B be closed after x mins. Then sum of works done by A and B = 1. \$12/16 + x/32 = 1\$. Solving, we get x = 8.

### Question 5

A tank is (2/9)th filled with water. When 64 liters of water are added, it becomes (2/5)th filled. What is the capacity of the tank?

A

360 liters.

B

370 liters.

C

380 liters.

D

390 liters.

Soln.
Ans: a

Let x be the capacity in liters. \${2x}/9 + 64 = {2x}/5\$. Solving, x = 360 liters.