# Pipes and Cisterns Quiz Set 013

### Question 1

Two pipes can together fill a cistern in 5 minutes. How long does the slower alone take if the speeds of the pipes are in the ratio 4 : 1?

A

25 mins.

B

26 mins.

C

24 mins.

D

27 mins.

Soln.
Ans: a

Let the time taken by the slower pipe alone be x. Then 5 × \$(1/x + 4/x)\$ = 1. Solving for x, we get x = 5 × 5 = 25 mins.

### Question 2

Two taps X, Y and Z can fill a tank in 18, 17 and 10 minutes respectively. All the taps are turned on at the same time. After how many minutes is the tank completely filled?

A

\$4{109/164}\$ mins.

B

\$5{114/163}\$ mins.

C

\$3{103/166}\$ mins.

D

\$7{95/166}\$ mins.

Soln.
Ans: a

Let the time be x mins. Then sum of works done by X, Y and Z = 1. \$x/18 + x/17 + x/10 = 1\$. Solving, we get x = \$4{109/164}\$. 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 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 pipes, A and B, can fill a cistern in 14 and 16 mins respectively. There is a leakage tap that can drain 7 liters of water per minute. If all three of them work together, the tank is filled in 18 minutes. What is the volume of the tank?

A

\$89{25/79}\$ liters.

B

\$91{37/78}\$ liters.

C

\$86{11/81}\$ liters.

D

\$90{1/27}\$ liters.

Soln.
Ans: a

Work done by the leakage in 1 min is \$1/14 + 1/16 - 1/18\$ = \${79/1008}\$. This work is equivalent to a volume of 7 liters. So, the total volume is 7 × \${1008/79}\$ = \${7056/79}\$, which is same as: \$89{25/79}\$ liters.

### Question 5

Two pipes, A and B, can fill a bucket in 11 and 15 mins respectively. Both the pipes are opened simultaneously. The bucket is filled in 8 mins if B is turned off after how many minutes:

A

\$4{1/11}\$ mins.

B

\$5{3/5}\$ mins.

C

\$2{8/13}\$ mins.

D

6 mins.

Soln.
Ans: a

Let B be closed after it has been filling for x minutes. Work done by pipes A and B should add to 1. So \$8/11\$ + \$x/15\$ = 1. Solving, we get x = \${45/11}\$, which is same as: \$4{1/11}\$. 