# Pipes and Cisterns Quiz Set 006

### Question 1

Tap X can fill the tank in 16 mins. Tap Y can empty it in 12 mins. In how many minutes will the tank be emptied if both the taps are opened together when the tank is \$9/18\$th full of water?

A

24 mins.

B

25 mins.

C

23 mins.

D

9 mins.

Soln.
Ans: a

1 filled tank can be emptied in \${16 × 12}/{16 - 12}\$ mins. So 9/18 can be emptied in \${16 × 12}/{16 - 12}\$ × \$9/18\$ = 24 mins.

### Question 2

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 3

Tap X can fill the tank in 11 mins. Tap Y can empty it in 5 mins. In how many minutes will the tank be emptied if both the taps are opened together when the tank is \$8/10\$th full of water?

A

\$7{1/3}\$ mins.

B

\$12{1/2}\$ mins.

C

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

D

\$6{1/5}\$ mins.

Soln.
Ans: a

1 filled tank can be emptied in \${11 × 5}/{11 - 5}\$ mins. So 8/10 can be emptied in \${11 × 5}/{11 - 5}\$ × \$8/10\$ = \${22/3}\$, which is same as: \$7{1/3}\$ mins.

### Question 4

One tap can fill a tank 2 times faster than the other. If they together fill it in 9 minutes, how much time does the slower alone take to fill the tank?

A

27 mins.

B

3 mins.

C

4 mins.

D

5 mins.

Soln.
Ans: a

Let the one minute work of the taps be 1/x and 2/x. We have \$1/x + 2/x = 1/9\$, which gives x = 3 × 9 = 27 mins.

### Question 5

Three taps R, G and B are supplying red, green and blue colored inks into a tub. They can independently fill the tub in 7, 3 and 6 minutes. They are turned on at the same time. What is the ratio of blue ink after 3 minutes?

A

\${7/27}\$.

B

\$1{4/13}\$.

C

\${7/29}\$.

D

\$3{1/29}\$.

Soln.
Ans: a

Let the time taken by them to independently fill the tank be r, g and b minutes. Ink discharged by the blue tap is \$3/b\$. The total of all the inks is \$3/r + 3/g + 3/b\$. The ratio is \${1/b}/{1/r + 1/g + 1/b}\$, which simplifies to \${rg}/{rg + gb + br}\$ = \${7/27}\$.