Electronics and Communication Engineering (ECE) Exam > Electronics and Communication Engineering (ECE) Questions > If the arithmetic mean of two numbers is 10 a...
Start Learning for Free
If the arithmetic mean of two numbers is 10 and their geometric mean is 8, the numbers are
- a)12, 18
- b)16, 4
- c)15, 5
- d)20, 5
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If the arithmetic mean of two numbers is 10 and their geometric mean i...
Let the numbers be a and b Then
Solving a + b = 20 and a - b = 12 we get a = 16 and b = 4.
Most Upvoted Answer
If the arithmetic mean of two numbers is 10 and their geometric mean i...
Arithmetic mean is addition of two numbers and geometric mean is square root of their product,, equate both equations and u will get answer.
Free Test
FREE
| Start Free Test |
Community Answer
If the arithmetic mean of two numbers is 10 and their geometric mean i...
To solve this problem, we need to use the formulas for arithmetic mean and geometric mean.
The arithmetic mean (AM) of two numbers is the sum of the numbers divided by 2.
The geometric mean (GM) of two numbers is the square root of their product.
Let's assume the two numbers are x and y.
1. Set up the equations:
- The arithmetic mean is 10, so we have (x + y)/2 = 10.
- The geometric mean is 8, so we have √(xy) = 8.
2. Solve for one variable in terms of the other:
From the first equation, we can isolate one variable:
x + y = 20
y = 20 - x
3. Substitute the expression for y into the second equation:
√(x(20 - x)) = 8
4. Square both sides of the equation to eliminate the square root:
x(20 - x) = 64
5. Expand and rearrange the equation:
20x - x^2 = 64
x^2 - 20x + 64 = 0
6. Factor the quadratic equation:
(x - 16)(x - 4) = 0
7. Set each factor equal to zero and solve for x:
x - 16 = 0 or x - 4 = 0
x = 16 or x = 4
8. Substitute the values of x back into the equation y = 20 - x:
If x = 16, then y = 20 - 16 = 4
If x = 4, then y = 20 - 4 = 16
Therefore, the two numbers are 16 and 4, which matches option 'B' (16, 4).
So, option 'B' is the correct answer.
The arithmetic mean (AM) of two numbers is the sum of the numbers divided by 2.
The geometric mean (GM) of two numbers is the square root of their product.
Let's assume the two numbers are x and y.
1. Set up the equations:
- The arithmetic mean is 10, so we have (x + y)/2 = 10.
- The geometric mean is 8, so we have √(xy) = 8.
2. Solve for one variable in terms of the other:
From the first equation, we can isolate one variable:
x + y = 20
y = 20 - x
3. Substitute the expression for y into the second equation:
√(x(20 - x)) = 8
4. Square both sides of the equation to eliminate the square root:
x(20 - x) = 64
5. Expand and rearrange the equation:
20x - x^2 = 64
x^2 - 20x + 64 = 0
6. Factor the quadratic equation:
(x - 16)(x - 4) = 0
7. Set each factor equal to zero and solve for x:
x - 16 = 0 or x - 4 = 0
x = 16 or x = 4
8. Substitute the values of x back into the equation y = 20 - x:
If x = 16, then y = 20 - 16 = 4
If x = 4, then y = 20 - 4 = 16
Therefore, the two numbers are 16 and 4, which matches option 'B' (16, 4).
So, option 'B' is the correct answer.
Attention Electronics and Communication Engineering (ECE) Students!
To make sure you are not studying endlessly, EduRev has designed Electronics and Communication Engineering (ECE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Electronics and Communication Engineering (ECE).
|
Explore Courses for Electronics and Communication Engineering (ECE) exam
|
|
Similar Electronics and Communication Engineering (ECE) Doubts
Top Courses for Electronics and Communication Engineering (ECE)View all
If the arithmetic mean of two numbers is 10 and their geometric mean is 8, the numbers area)12, 18b)16, 4c)15, 5d)20, 5Correct answer is option 'B'. Can you explain this answer?
Question Description
If the arithmetic mean of two numbers is 10 and their geometric mean is 8, the numbers area)12, 18b)16, 4c)15, 5d)20, 5Correct answer is option 'B'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about If the arithmetic mean of two numbers is 10 and their geometric mean is 8, the numbers area)12, 18b)16, 4c)15, 5d)20, 5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the arithmetic mean of two numbers is 10 and their geometric mean is 8, the numbers area)12, 18b)16, 4c)15, 5d)20, 5Correct answer is option 'B'. Can you explain this answer?.
If the arithmetic mean of two numbers is 10 and their geometric mean is 8, the numbers area)12, 18b)16, 4c)15, 5d)20, 5Correct answer is option 'B'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about If the arithmetic mean of two numbers is 10 and their geometric mean is 8, the numbers area)12, 18b)16, 4c)15, 5d)20, 5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the arithmetic mean of two numbers is 10 and their geometric mean is 8, the numbers area)12, 18b)16, 4c)15, 5d)20, 5Correct answer is option 'B'. Can you explain this answer?.
Solutions for If the arithmetic mean of two numbers is 10 and their geometric mean is 8, the numbers area)12, 18b)16, 4c)15, 5d)20, 5Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE).
Download more important topics, notes, lectures and mock test series for Electronics and Communication Engineering (ECE) Exam by signing up for free.
Here you can find the meaning of If the arithmetic mean of two numbers is 10 and their geometric mean is 8, the numbers area)12, 18b)16, 4c)15, 5d)20, 5Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the arithmetic mean of two numbers is 10 and their geometric mean is 8, the numbers area)12, 18b)16, 4c)15, 5d)20, 5Correct answer is option 'B'. Can you explain this answer?, a detailed solution for If the arithmetic mean of two numbers is 10 and their geometric mean is 8, the numbers area)12, 18b)16, 4c)15, 5d)20, 5Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of If the arithmetic mean of two numbers is 10 and their geometric mean is 8, the numbers area)12, 18b)16, 4c)15, 5d)20, 5Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the arithmetic mean of two numbers is 10 and their geometric mean is 8, the numbers area)12, 18b)16, 4c)15, 5d)20, 5Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Electronics and Communication Engineering (ECE) tests.
|
|
Explore Courses for Electronics and Communication Engineering (ECE) 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.
x
![]()
For Your Perfect Score in Electronics and Communication Engineering (ECE)
The Best you need at One Place
|
© 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