Pipes and Cisterns Quiz Set 003

Question 1

Pipe A can fill a cistern in 60 minutes, while the pipe B can fill it in 40 minutes. They are alternately open for 1 minute. How long will it take the cistern to fill completely?

A

48 mins.

B

49 mins.

C

47 mins.

D

50 mins.

Soln.
Ans: a

Let the total time taken be 2x minutes. Both X and Y run for x mins. So \$(x/40 + x/60)\$ = 1. Solving for x, we get x = 24, which gives 2x = 48.

Question 2

Two pipes, A and B, can fill a cistern in 8 and 16 mins respectively. There is a leakage tap that can drain 16 liters of water per minute. If all three of them work together, the tank is filled in 15 minutes. What is the volume of the tank?

A

\$132{12/29}\$ liters.

B

\$138{5/28}\$ liters.

C

\$122{29/31}\$ liters.

D

\$126{21/31}\$ liters.

Soln.
Ans: a

Work done by the leakage in 1 min is \$1/8 + 1/16 - 1/15\$ = \${29/240}\$. This work is equivalent to a volume of 16 liters. So, the total volume is 16 × \${240/29}\$ = \${3840/29}\$, which is same as: \$132{12/29}\$ liters.

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 ink dispensers discharge ink into a color mixer. The first one can fill it in 22 minutes, whereas the second can fill it in 11 minutes. Both them are opened at the same time, but the second ink dispenser is turned off after 5 minutes. What is the total time required to fill the color mixer cistern?

A

12 mins.

B

13 mins.

C

11 mins.

D

14 mins.

Soln.
Ans: a

If the total time is T, the sum of works done by the ink dispensers are \$T/22 + 5/11\$ = 1. Solving, T = 12 mins.

Question 5

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. 