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### Question 1

A tank is filled in 13 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**

a^{3} - 39a^{2} - ad^{2} + 13d^{2} = 0.

**B**

a^{3} - 26a^{2} + ad^{2} + 13d^{2} = 0.

**C**

a^{3} - 13a^{2} - ad^{2} + 13d^{2} = 0.

**D**

a^{3} - 65a^{2} + ad^{2} + 13d^{2} = 0.

**Soln.**

**Ans: a**

Let the times taken by the three taps be a - d, a and a + d. Then 13 minutes work of all the taps should add to 1. So we have, $13 × 1/{a - d} + 13 × 1/a + 13 × 1/{a + d}$ = 1, which is same as a^{3} - 39a^{2} - ad^{2} + 13d^{2} = 0.

### Question 2

A tank is filled in $1{2/13}$ minutes by three taps running together. Times taken by the three taps to independently fill the tank are in an AP[Arithmetic Progression]. If the first tap is a leakage tap and the second tap takes 1 minute to fill the tank, then, the common difference of the AP can be?

**A**

4.

**B**

5.

**C**

3.

**D**

6.

**Soln.**

**Ans: a**

Let the times taken by the three taps be 1 - d, 1 and 1 + d. The time taken by the first tap will be negative because it is a leakage tap. Then ${15/13}$ minutes work of all the taps should add to 1. So we have, ${15/13}$ × $(1/{1 - d} + 1/1 + 1/{1 + d})$ = 1, which is same as $2/{1 - d^2} + 1$ = ${13/15}$. Solving we get d = ±4.

### Question 3

A bucket can be filled by a tap in 2 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?

### Question 4

Two pipes, A and B, can fill a bucket in 17 and 9 mins respectively. Both the pipes are opened simultaneously. The bucket is filled in 7 mins if B is turned off after how many minutes:

**A**

$5{5/17}$ mins.

**B**

$6{11/16}$ mins.

**C**

$3{16/19}$ mins.

**D**

$7{8/19}$ 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 $7/17$ + $x/9$ = 1. Solving, we get x = ${90/17}$, which is same as: $5{5/17}$.

### Question 5

Tap X can fill the tank in 18 mins. Tap Y can empty it in 9 mins. In how many minutes will the tank be emptied if both the taps are opened together when the tank is $5/17$^{th} full of water?

This Blog Post/Article "Pipes and Cisterns Quiz Set 012" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2019-08-18.