JEE Exam > JEE Questions > The sum of two positive numbers is 20. Find t...
Start Learning for Free
The sum of two positive numbers is 20. Find the numbers if their product is maximum
- a)5,15
- b)8,12
- c)20,0
- d)10,10
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The sum of two positive numbers is 20. Find the numbers if their produ...
Given:
The sum of two positive numbers is 20.
To find:
The numbers if their product is maximum.
Approach:
To find the numbers, we need to maximize their product while satisfying the condition that their sum is 20. We can solve this problem by using the concept of the arithmetic mean-geometric mean inequality.
The arithmetic mean-geometric mean inequality states that for any two positive numbers, their arithmetic mean is always greater than or equal to their geometric mean. Mathematically, it can be expressed as:
AM ≥ GM
Where AM denotes the arithmetic mean and GM denotes the geometric mean.
Solution:
Let's consider the two positive numbers as 'a' and 'b'.
1. Consider the case of a = 5 and b = 15:
- Sum of the numbers: 5 + 15 = 20
- Product of the numbers: 5 * 15 = 75
2. Consider the case of a = 8 and b = 12:
- Sum of the numbers: 8 + 12 = 20
- Product of the numbers: 8 * 12 = 96
3. Consider the case of a = 20 and b = 0:
- Sum of the numbers: 20 + 0 = 20
- Product of the numbers: 20 * 0 = 0
4. Consider the case of a = 10 and b = 10:
- Sum of the numbers: 10 + 10 = 20
- Product of the numbers: 10 * 10 = 100
Conclusion:
From the above calculations, we can see that the product of the numbers is maximum when a = 10 and b = 10. Therefore, the correct answer is option 'D'.
The sum of two positive numbers is 20.
To find:
The numbers if their product is maximum.
Approach:
To find the numbers, we need to maximize their product while satisfying the condition that their sum is 20. We can solve this problem by using the concept of the arithmetic mean-geometric mean inequality.
The arithmetic mean-geometric mean inequality states that for any two positive numbers, their arithmetic mean is always greater than or equal to their geometric mean. Mathematically, it can be expressed as:
AM ≥ GM
Where AM denotes the arithmetic mean and GM denotes the geometric mean.
Solution:
Let's consider the two positive numbers as 'a' and 'b'.
1. Consider the case of a = 5 and b = 15:
- Sum of the numbers: 5 + 15 = 20
- Product of the numbers: 5 * 15 = 75
2. Consider the case of a = 8 and b = 12:
- Sum of the numbers: 8 + 12 = 20
- Product of the numbers: 8 * 12 = 96
3. Consider the case of a = 20 and b = 0:
- Sum of the numbers: 20 + 0 = 20
- Product of the numbers: 20 * 0 = 0
4. Consider the case of a = 10 and b = 10:
- Sum of the numbers: 10 + 10 = 20
- Product of the numbers: 10 * 10 = 100
Conclusion:
From the above calculations, we can see that the product of the numbers is maximum when a = 10 and b = 10. Therefore, the correct answer is option 'D'.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The sum of two positive numbers is 20. Find the numbers if their product is maximuma)5,15b)8,12c)20,0d)10,10Correct answer is option 'D'. Can you explain this answer?
Question Description
The sum of two positive numbers is 20. Find the numbers if their product is maximuma)5,15b)8,12c)20,0d)10,10Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The sum of two positive numbers is 20. Find the numbers if their product is maximuma)5,15b)8,12c)20,0d)10,10Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of two positive numbers is 20. Find the numbers if their product is maximuma)5,15b)8,12c)20,0d)10,10Correct answer is option 'D'. Can you explain this answer?.
The sum of two positive numbers is 20. Find the numbers if their product is maximuma)5,15b)8,12c)20,0d)10,10Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The sum of two positive numbers is 20. Find the numbers if their product is maximuma)5,15b)8,12c)20,0d)10,10Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of two positive numbers is 20. Find the numbers if their product is maximuma)5,15b)8,12c)20,0d)10,10Correct answer is option 'D'. Can you explain this answer?.
Solutions for The sum of two positive numbers is 20. Find the numbers if their product is maximuma)5,15b)8,12c)20,0d)10,10Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The sum of two positive numbers is 20. Find the numbers if their product is maximuma)5,15b)8,12c)20,0d)10,10Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The sum of two positive numbers is 20. Find the numbers if their product is maximuma)5,15b)8,12c)20,0d)10,10Correct answer is option 'D'. Can you explain this answer?, a detailed solution for The sum of two positive numbers is 20. Find the numbers if their product is maximuma)5,15b)8,12c)20,0d)10,10Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of The sum of two positive numbers is 20. Find the numbers if their product is maximuma)5,15b)8,12c)20,0d)10,10Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The sum of two positive numbers is 20. Find the numbers if their product is maximuma)5,15b)8,12c)20,0d)10,10Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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!
within 7 days!
Takes less than 10 seconds to signup