# Pipes and Cisterns Quiz Set 009

### Question 1

A tap can fill a tank in 2 hours. Because of a leak it took 3 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

6 hrs.

B

7 hrs.

C

5 hrs.

D

3 hrs.

Soln.
Ans: a

Work done by the leak in one hour is \$1/2 - 1/({18/6})\$ = \$1/2 - 6/18\$ = \$6/36\$. So the leak will complete the whole task in 6 hours.

### Question 2

A bucket can be filled by a tap in 7 minutes. Another tap on the same bucket can empty it in 9 mins. How long will it take to fill the bucket if both the taps are opened together?

A

\$31{1/2}\$ mins.

B

\$32{1/2}\$ mins.

C

\$30{1/2}\$ mins.

D

\$17{1/4}\$ 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)\$ = \${7 × 9}/{9 - 7}\$ = \${63/2}\$, which is same as: \$31{1/2}\$ mins.

### Question 3

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 4

Two ink dispensers discharge ink into a color mixer. The first one can fill it in 35 minutes, whereas the second can fill it in 7 minutes. Both them are opened at the same time, but the second ink dispenser is turned off after 4 minutes. What is the total time required to fill the color mixer cistern?

A

15 mins.

B

16 mins.

C

14 mins.

D

17 mins.

Soln.
Ans: a

If the total time is T, the sum of works done by the ink dispensers are \$T/35 + 4/7\$ = 1. Solving, T = 15 mins.

### Question 5

A tank is (2/9)th filled with water. When 108 liters of water are added, it becomes (2/3)th filled. What is the capacity of the tank?

A

243 liters.

B

253 liters.

C

263 liters.

D

273 liters.

Soln.
Ans: a

Let x be the capacity in liters. \${2x}/9 + 108 = {2x}/3\$. Solving, x = 243 liters. 