Correct Answers: | |

Wrong Answers: | |

Unattempted: |

### Question 1

A tank is filled in $1{2/33}$ 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**

6.

**B**

7.

**C**

5.

**D**

8.

**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 ${35/33}$ minutes work of all the taps should add to 1. So we have, ${35/33}$ × $(1/{1 - d} + 1/1 + 1/{1 + d})$ = 1, which is same as $2/{1 - d^2} + 1$ = ${33/35}$. Solving we get d = ±6.

### Question 2

A tank is (2/5)^{th} filled with water. When 44 liters of water are added, it becomes (8/9)^{th} filled. What is the capacity of the tank?

### Question 3

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?

### Question 4

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**

a^{3} - 33a^{2} - ad^{2} + 11d^{2} = 0.

**B**

a^{3} - 22a^{2} + ad^{2} + 11d^{2} = 0.

**C**

a^{3} - 11a^{2} - ad^{2} + 11d^{2} = 0.

**D**

a^{3} - 55a^{2} + ad^{2} + 11d^{2} = 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 a^{3} - 33a^{2} - ad^{2} + 11d^{2} = 0.

### Question 5

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?

### More Chapters | See All...

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This Blog Post/Article "Pipes and Cisterns Quiz Set 006" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2020-01-14.