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Two number A and 8 are such that their GM is 20% lower than their AM. Find the ratio between the numbers.
- a)3 : 2
- b)4 : 1
- c)2 : 1
- d)3 : 1
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two number A and 8 are such that their GM is 20% lower than their AM....
(a+b)/2 = AM
Here it is given that GM = 20% less than AM, that is
GM = 4/5 AM
only possibility is a = 1 & b = 4 or a = 4, b = 1
So, ratio is 4 :1
Most Upvoted Answer
Two number A and 8 are such that their GM is 20% lower than their AM....
Given, the GM (geometric mean) of two numbers A and 8 is 20% lower than their AM (arithmetic mean).
Let A be the first number and 8 be the second number.
We know that,
GM of A and 8 = √(A x 8)
AM of A and 8 = (A + 8)/2
According to the given condition,
GM of A and 8 = 0.8 × AM of A and 8
√(A x 8) = 0.8 × (A + 8)/2
2√(A x 8) = 0.8 × (A + 8)
√(A x 8) = 0.4 × (A + 8)
Squaring both sides, we get
A x 8 = 0.16 (A^2 + 16A + 64)
0.16A^2 - 0.48A - 64 = 0
A^2 - 3A - 400 = 0
Solving this quadratic equation, we get A = 20 or A = - 20
Since we cannot have a negative number, we take A = 20.
So, the two numbers are 20 and 8.
Ratio of the two numbers = 20 : 8
= 5 : 2
Therefore, the correct answer is option (B) 4 : 1.
Let A be the first number and 8 be the second number.
We know that,
GM of A and 8 = √(A x 8)
AM of A and 8 = (A + 8)/2
According to the given condition,
GM of A and 8 = 0.8 × AM of A and 8
√(A x 8) = 0.8 × (A + 8)/2
2√(A x 8) = 0.8 × (A + 8)
√(A x 8) = 0.4 × (A + 8)
Squaring both sides, we get
A x 8 = 0.16 (A^2 + 16A + 64)
0.16A^2 - 0.48A - 64 = 0
A^2 - 3A - 400 = 0
Solving this quadratic equation, we get A = 20 or A = - 20
Since we cannot have a negative number, we take A = 20.
So, the two numbers are 20 and 8.
Ratio of the two numbers = 20 : 8
= 5 : 2
Therefore, the correct answer is option (B) 4 : 1.
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Two number A and 8 are such that their GM is 20% lower than their AM. Find the ratio between the numbers.a)3 : 2b)4 : 1c)2 : 1d)3 : 1Correct answer is option 'B'. Can you explain this answer?
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