# Pipes and Cisterns Quiz Set 020

### Question 1

Two taps X, Y and Z can fill a tank in 5, 17 and 4 minutes respectively. All the taps are turned on at the same time. After how many minutes is the tank completely filled?

A

\$1{167/173}\$ mins.

B

\$2{169/172}\$ mins.

C

\${167/175}\$ mins.

D

\$4{159/175}\$ mins.

Soln.
Ans: a

Let the time be x mins. Then sum of works done by X, Y and Z = 1. \$x/5 + x/17 + x/4 = 1\$. Solving, we get x = \$1{167/173}\$. Or use the shortcut \${abc}/{ab + bc + ca}\$. Another thing, instead of solving the entire calculation, you can keep an eye on the options to find the nearest answer.

### Question 2

Two pipes, A and B, can fill a cistern in 5 and 8 mins respectively. There is a leakage tap that can drain 8 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

\$30{30/31}\$ liters.

B

\$33{1/30}\$ liters.

C

\$28{5/33}\$ liters.

D

\$31{10/11}\$ liters.

Soln.
Ans: a

Work done by the leakage in 1 min is \$1/5 + 1/8 - 1/15\$ = \${31/120}\$. This work is equivalent to a volume of 8 liters. So, the total volume is 8 × \${120/31}\$ = \${960/31}\$, which is same as: \$30{30/31}\$ liters.

### Question 3

A tank is filled in 19 minutes by three taps running together. Tap A is twice as fast as tap B, and tap B is twice as fast as tap C. How much time will tap A take to fill the tank?

A

133 mins.

B

134 mins.

C

132 mins.

D

135 mins.

Soln.
Ans: a

Let the time taken by tap A be x mins. Then 19 minutes work of all the taps should add to 1. So we have, \$19 × 1/x + 19 × 2/x + 19 × 4/x\$ = 1, which is same as \$19 × 7/x\$ = 1. Solving, we get x = 133 mins.

### Question 4

A bucket can be filled by a tap in 6 minutes. Another tap on the same bucket can empty it in 15 mins. How long will it take to fill the bucket if both the taps are opened together?

A

10 mins.

B

11 mins.

C

9 mins.

D

\$4{1/3}\$ 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)\$ = \${6 × 15}/{15 - 6}\$ = 10 mins.

### Question 5

Two pipes can together fill a cistern in 7 minutes. How long does the slower alone take if the speeds of the pipes are in the ratio 4 : 1?

A

35 mins.

B

36 mins.

C

34 mins.

D

37 mins.

Soln.
Ans: a

Let the time taken by the slower pipe alone be x. Then 7 × \$(1/x + 4/x)\$ = 1. Solving for x, we get x = 7 × 5 = 35 mins. 