Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > A reservoir will be filled in 12 hours if tw...
Start Learning for Free
A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?
- a)35 hours
- b)30 hours
- c)28 hours
- d)20 hours
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A reservoir will be filled in 12 hours if two pipes function simultan...
Let the first pipe fill the reservoir in x hours.
Then, the second pipe can fill the reservoir in x – 10 hours.
Now, according to the question,
1/x + 1/(x-10) = 1/12
⇒ 12(x – 10 + x) = x2 – 10x
⇒24x – 120 = x2 – 10x
⇒x2 – 34x + 120 = 0
⇒x2 – 30x - 4x + 120 = 0
⇒(x – 30)(x – 4) = 0
⇒x = 30, 4
But, x ≠ 4 (∵ x – 10 should be positive)
∴ x = 30 hours
x – 10 = 20 hours
Free Test
FREE
| Start Free Test |
Community Answer
A reservoir will be filled in 12 hours if two pipes function simultan...
Let's assume that the first pipe can fill the reservoir in x hours.
Given that the second pipe fills the reservoir 10 hours faster than the first pipe, the second pipe can fill the reservoir in (x - 10) hours.
To find the time taken by both pipes working together, we can use the concept of rates. The rate at which the first pipe fills the reservoir is 1/x (as it fills the reservoir in x hours), and the rate at which the second pipe fills the reservoir is 1/(x - 10) (as it fills the reservoir in x - 10 hours).
When both pipes work simultaneously, their rates add up. So, the combined rate of both pipes is 1/x + 1/(x - 10).
The reservoir will be filled in 12 hours when both pipes work simultaneously. So, the combined rate of both pipes is 1/12.
Therefore, we can write the equation as:
1/x + 1/(x - 10) = 1/12
To solve this equation, we can multiply through by the common denominator, which is 12x(x - 10):
12(x - 10) + 12x = x(x - 10)
Expanding and simplifying the equation:
12x - 120 + 12x = x^2 - 10x
24x - 120 = x^2 - 10x
Rearranging the equation and setting it equal to zero:
x^2 - 34x + 120 = 0
Factoring the quadratic equation:
(x - 20)(x - 6) = 0
Solving for x, we get two possible solutions: x = 20 and x = 6.
Since the second pipe takes 10 hours less than the first pipe, the second pipe cannot take more time than the first pipe. Therefore, we can eliminate x = 20 as a valid solution.
Hence, the first pipe takes 6 hours to fill the reservoir, and the second pipe takes 6 - 10 = -4 hours, which is not possible.
Therefore, the only valid solution is x = 6, which means the second pipe takes 6 - 10 = -4 hours.
Therefore, the second pipe takes 20 hours to fill the reservoir (Option D).
Given that the second pipe fills the reservoir 10 hours faster than the first pipe, the second pipe can fill the reservoir in (x - 10) hours.
To find the time taken by both pipes working together, we can use the concept of rates. The rate at which the first pipe fills the reservoir is 1/x (as it fills the reservoir in x hours), and the rate at which the second pipe fills the reservoir is 1/(x - 10) (as it fills the reservoir in x - 10 hours).
When both pipes work simultaneously, their rates add up. So, the combined rate of both pipes is 1/x + 1/(x - 10).
The reservoir will be filled in 12 hours when both pipes work simultaneously. So, the combined rate of both pipes is 1/12.
Therefore, we can write the equation as:
1/x + 1/(x - 10) = 1/12
To solve this equation, we can multiply through by the common denominator, which is 12x(x - 10):
12(x - 10) + 12x = x(x - 10)
Expanding and simplifying the equation:
12x - 120 + 12x = x^2 - 10x
24x - 120 = x^2 - 10x
Rearranging the equation and setting it equal to zero:
x^2 - 34x + 120 = 0
Factoring the quadratic equation:
(x - 20)(x - 6) = 0
Solving for x, we get two possible solutions: x = 20 and x = 6.
Since the second pipe takes 10 hours less than the first pipe, the second pipe cannot take more time than the first pipe. Therefore, we can eliminate x = 20 as a valid solution.
Hence, the first pipe takes 6 hours to fill the reservoir, and the second pipe takes 6 - 10 = -4 hours, which is not possible.
Therefore, the only valid solution is x = 6, which means the second pipe takes 6 - 10 = -4 hours.
Therefore, the second pipe takes 20 hours to fill the reservoir (Option D).
Attention Electrical Engineering (EE) Students!
To make sure you are not studying endlessly, EduRev has designed Electrical Engineering (EE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Electrical Engineering (EE).
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Top Courses for Electrical Engineering (EE)View all
A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?a)35 hoursb)30 hoursc)28 hoursd)20 hoursCorrect answer is option 'D'. Can you explain this answer?
Question Description
A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?a)35 hoursb)30 hoursc)28 hoursd)20 hoursCorrect answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?a)35 hoursb)30 hoursc)28 hoursd)20 hoursCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?a)35 hoursb)30 hoursc)28 hoursd)20 hoursCorrect answer is option 'D'. Can you explain this answer?.
A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?a)35 hoursb)30 hoursc)28 hoursd)20 hoursCorrect answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?a)35 hoursb)30 hoursc)28 hoursd)20 hoursCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?a)35 hoursb)30 hoursc)28 hoursd)20 hoursCorrect answer is option 'D'. Can you explain this answer?.
Solutions for A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?a)35 hoursb)30 hoursc)28 hoursd)20 hoursCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free.
Here you can find the meaning of A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?a)35 hoursb)30 hoursc)28 hoursd)20 hoursCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?a)35 hoursb)30 hoursc)28 hoursd)20 hoursCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?a)35 hoursb)30 hoursc)28 hoursd)20 hoursCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?a)35 hoursb)30 hoursc)28 hoursd)20 hoursCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?a)35 hoursb)30 hoursc)28 hoursd)20 hoursCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
|
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup