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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?
6.
7.
5.
8.
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?
a3 - 33a2 - ad2 + 11d2 = 0.
a3 - 22a2 + ad2 + 11d2 = 0.
a3 - 11a2 - ad2 + 11d2 = 0.
a3 - 55a2 + ad2 + 11d2 = 0.
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 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?
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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 2020-02-07. Published on: 2016-05-05