Railways Exam > Railways Questions > Sum of a fraction and thrice of its reciproca...
Start Learning for Free
Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?
- a)4/5
- b)9/4
- c)4/9
- d)5/4
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Sum of a fraction and thrice of its reciprocal is 73/20. What is the f...
Let the fraction be x.
Reciprocal = 1/x
Then,
x + 3/x = 73/20
⇒ x2 + 3 = 73x/20
⇒ 20x2 – 73x + 60 = 0
⇒ x = {- (-73) + √ (5329 – 4800)}/40 or x = {- (-73) - √ (5329 – 4800)}/40
⇒ x = 96/40 = 12/5 or x = 50/40 = 5/4
∴ the required fraction is 5/4 or 12/5.
Most Upvoted Answer
Sum of a fraction and thrice of its reciprocal is 73/20. What is the f...
To solve this problem, let's assume the fraction as x/y, where x and y are positive integers.
According to the given information, the sum of the fraction and thrice of its reciprocal is 73/20:
(x/y) + 3(y/x) = 73/20
To simplify this equation, let's get rid of the fractions by multiplying both sides by xy:
xy(x/y) + 3xy(y/x) = 73/20 * xy
This simplifies to:
x^2 + 3y^2 = 73/20 * xy
Now, let's multiply both sides by 20 to get rid of the fraction:
20x^2 + 60y^2 = 73xy
Next, let's rearrange the equation to get it in a quadratic form:
20x^2 - 73xy + 60y^2 = 0
This equation can be factored as:
(5x - 12y)(4x - 5y) = 0
Now we have two possible solutions:
1) 5x - 12y = 0
2) 4x - 5y = 0
Let's solve these two equations separately:
1) 5x - 12y = 0
Rearranging, we get:
5x = 12y
x/y = 12/5
2) 4x - 5y = 0
Rearranging, we get:
4x = 5y
x/y = 5/4
So, the possible fractions are x/y = 12/5 and x/y = 5/4.
However, the question asks for the fraction, not the ratio. Therefore, the correct answer is x/y = 5/4, which is option D.
According to the given information, the sum of the fraction and thrice of its reciprocal is 73/20:
(x/y) + 3(y/x) = 73/20
To simplify this equation, let's get rid of the fractions by multiplying both sides by xy:
xy(x/y) + 3xy(y/x) = 73/20 * xy
This simplifies to:
x^2 + 3y^2 = 73/20 * xy
Now, let's multiply both sides by 20 to get rid of the fraction:
20x^2 + 60y^2 = 73xy
Next, let's rearrange the equation to get it in a quadratic form:
20x^2 - 73xy + 60y^2 = 0
This equation can be factored as:
(5x - 12y)(4x - 5y) = 0
Now we have two possible solutions:
1) 5x - 12y = 0
2) 4x - 5y = 0
Let's solve these two equations separately:
1) 5x - 12y = 0
Rearranging, we get:
5x = 12y
x/y = 12/5
2) 4x - 5y = 0
Rearranging, we get:
4x = 5y
x/y = 5/4
So, the possible fractions are x/y = 12/5 and x/y = 5/4.
However, the question asks for the fraction, not the ratio. Therefore, the correct answer is x/y = 5/4, which is option D.
Attention Railways Students!
To make sure you are not studying endlessly, EduRev has designed Railways study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Railways.
|
Explore Courses for Railways exam
|
|
Similar Railways Doubts
Top Courses for RailwaysView all
Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?a)4/5b)9/4c)4/9d)5/4Correct answer is option 'D'. Can you explain this answer?
Question Description
Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?a)4/5b)9/4c)4/9d)5/4Correct answer is option 'D'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?a)4/5b)9/4c)4/9d)5/4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?a)4/5b)9/4c)4/9d)5/4Correct answer is option 'D'. Can you explain this answer?.
Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?a)4/5b)9/4c)4/9d)5/4Correct answer is option 'D'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?a)4/5b)9/4c)4/9d)5/4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?a)4/5b)9/4c)4/9d)5/4Correct answer is option 'D'. Can you explain this answer?.
Solutions for Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?a)4/5b)9/4c)4/9d)5/4Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Railways.
Download more important topics, notes, lectures and mock test series for Railways Exam by signing up for free.
Here you can find the meaning of Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?a)4/5b)9/4c)4/9d)5/4Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?a)4/5b)9/4c)4/9d)5/4Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?a)4/5b)9/4c)4/9d)5/4Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?a)4/5b)9/4c)4/9d)5/4Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?a)4/5b)9/4c)4/9d)5/4Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Railways tests.
|
|
Explore Courses for Railways 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup