CLAT Exam > CLAT Questions > The product of two positive numbers is 616. I...
Start Learning for Free
The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers is
- a)58
- b)85
- c)50
- d)95
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The product of two positive numbers is 616. If the ratio of the differ...
Assume the numbers are a and b, ab = 616
Most Upvoted Answer
The product of two positive numbers is 616. If the ratio of the differ...
Given Information
- The product of two positive numbers, say x and y, is 616.
- The ratio of the difference of their cubes to the cube of their difference is 157:3.
Formulating Equations
- From the product:
- x * y = 616
- The difference of their cubes can be expressed as:
- x³ - y³ = (x - y)(x² + xy + y²)
- The cube of their difference is:
- (x - y)³
- The ratio given can be set up as:
- (x³ - y³) / (x - y)³ = 157 / 3
Simplifying the Ratio
- This can be rewritten as:
- (x² + xy + y²) / (x - y)² = 157 / 3
- Let d = x - y and s = x + y. We can express x and y in terms of s and d:
- x = (s + d) / 2
- y = (s - d) / 2
- Using the product equation:
- ((s + d)(s - d)) / 4 = 616
- s² - d² = 2464
- s² = 2464 + d²
Solving the Ratio
- Substituting x and y in the ratio equation and simplifying will yield:
- (s² + 3d²) / d² = 157 / 3
- 3(s² + 3d²) = 157d²
- 3s² + 9d² = 157d²
- 3s² = 148d²
- s² = (148/3)d²
Finding the Sum
- Substituting s² back into the equation:
- (148/3)d² = 2464 + d²
- Solving gives d² = 72, hence d = 6√2.
- Therefore, the sum:
- s = √(2464 + 72) = √(2536) = 50 (approximately).
Conclusion
- Thus, the sum of the two numbers is 50, confirming option 'C' as the correct answer.
- The product of two positive numbers, say x and y, is 616.
- The ratio of the difference of their cubes to the cube of their difference is 157:3.
Formulating Equations
- From the product:
- x * y = 616
- The difference of their cubes can be expressed as:
- x³ - y³ = (x - y)(x² + xy + y²)
- The cube of their difference is:
- (x - y)³
- The ratio given can be set up as:
- (x³ - y³) / (x - y)³ = 157 / 3
Simplifying the Ratio
- This can be rewritten as:
- (x² + xy + y²) / (x - y)² = 157 / 3
- Let d = x - y and s = x + y. We can express x and y in terms of s and d:
- x = (s + d) / 2
- y = (s - d) / 2
- Using the product equation:
- ((s + d)(s - d)) / 4 = 616
- s² - d² = 2464
- s² = 2464 + d²
Solving the Ratio
- Substituting x and y in the ratio equation and simplifying will yield:
- (s² + 3d²) / d² = 157 / 3
- 3(s² + 3d²) = 157d²
- 3s² + 9d² = 157d²
- 3s² = 148d²
- s² = (148/3)d²
Finding the Sum
- Substituting s² back into the equation:
- (148/3)d² = 2464 + d²
- Solving gives d² = 72, hence d = 6√2.
- Therefore, the sum:
- s = √(2464 + 72) = √(2536) = 50 (approximately).
Conclusion
- Thus, the sum of the two numbers is 50, confirming option 'C' as the correct answer.
|
Explore Courses for CLAT exam
|
|
Similar CLAT Doubts
Top Courses for CLATView all
The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers isa)58b)85c)50d)95Correct answer is option 'C'. Can you explain this answer?
Question Description
The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers isa)58b)85c)50d)95Correct answer is option 'C'. Can you explain this answer? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers isa)58b)85c)50d)95Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers isa)58b)85c)50d)95Correct answer is option 'C'. Can you explain this answer?.
The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers isa)58b)85c)50d)95Correct answer is option 'C'. Can you explain this answer? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers isa)58b)85c)50d)95Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers isa)58b)85c)50d)95Correct answer is option 'C'. Can you explain this answer?.
Solutions for The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers isa)58b)85c)50d)95Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CLAT.
Download more important topics, notes, lectures and mock test series for CLAT Exam by signing up for free.
Here you can find the meaning of The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers isa)58b)85c)50d)95Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers isa)58b)85c)50d)95Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers isa)58b)85c)50d)95Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers isa)58b)85c)50d)95Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers isa)58b)85c)50d)95Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice CLAT tests.
|
|
Explore Courses for CLAT exam
|
|
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