# Pipes and Cisterns Quiz Set 003

### Question 1

Two taps A and B can fill a tank in 16 and 32 minutes respectively. Both the taps are turned on at the same time. After how many minutes should B be turned off so that the tank can be filled in 12 minutes?

A

8 mins.

B

9 mins.

C

7 mins.

D

11 mins.

Soln.
Ans: a

Let B be closed after x mins. Then sum of works done by A and B = 1. \$12/16 + x/32 = 1\$. Solving, we get x = 8.

### Question 2

A tank is filled in 11 minutes by three taps running together. Times taken by the three taps independently are in an AP[Arithmetic Progression], whose first term is a and common difference d. Then, a and d satisfy the relation?

A

a3 - 33a2 - ad2 + 11d2 = 0.

B

a3 - 22a2 + ad2 + 11d2 = 0.

C

a3 - 11a2 - ad2 + 11d2 = 0.

D

a3 - 55a2 + ad2 + 11d2 = 0.

Soln.
Ans: a

Let the times taken by the three taps be a - d, a and a + d. Then 11 minutes work of all the taps should add to 1. So we have, \$11 × 1/{a - d} + 11 × 1/a + 11 × 1/{a + d}\$ = 1, which is same as a3 - 33a2 - ad2 + 11d2 = 0.

### Question 3

A tap can fill a tank in 2 hours. Because of a leak it took \$2{3/8}\$ 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

\$12{2/3}\$ hrs.

B

\$20{1/2}\$ hrs.

C

\$11{2/3}\$ hrs.

D

\$9{2/5}\$ hrs.

Soln.
Ans: a

Work done by the leak in one hour is \$1/2 - 1/({19/8})\$ = \$1/2 - 8/19\$ = \$3/38\$. So the leak will complete the whole task in \${38/3}\$, which is same as: \$12{2/3}\$ hours.

### Question 4

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 5

A tank is filled in 17 minutes by three taps running together. Times taken by the three taps independently are in an AP[Arithmetic Progression], whose first term is a and common difference d. Then, a and d satisfy the relation?

A

a3 - 51a2 - ad2 + 17d2 = 0.

B

a3 - 34a2 + ad2 + 17d2 = 0.

C

a3 - 17a2 - ad2 + 17d2 = 0.

D

a3 - 85a2 + ad2 + 17d2 = 0.

Soln.
Ans: a

Let the times taken by the three taps be a - d, a and a + d. Then 17 minutes work of all the taps should add to 1. So we have, \$17 × 1/{a - d} + 17 × 1/a + 17 × 1/{a + d}\$ = 1, which is same as a3 - 51a2 - ad2 + 17d2 = 0.