Correct option is C
Given:
Sum of two positive numbers = 40
The GM of these two numbers is 20% lower than their AM
Concept:
AM (Arithmetic Mean) = (a + b) / 2
GM (Geometric Mean) = √(a × b)
GM = 0.8 × AM
Solution:
Let the two numbers be a and b.
a + b = 40
AM = (a + b) / 2 = 40 / 2 = 20
GM = √(a × b)
Given GM = 0.8 × AM
=> √(a × b) = 0.8 × 20
=> √(a × b) = 16
=> a × b = 162
=> a × b = 256
We have the equations:
1. a + b = 40
2. a × b = 256
Solving these two equations:
Let a and b be the roots of the quadratic equation x2- (a+b)x + ab = 0
=> x2- 40x + 256 = 0
Solving for x using the quadratic formula x = [ -b ± √(b2- 4ac) ] / 2a
=> x = [ 40 ± √(1600 - 1024) ] / 2
=> x = [ 40 ± √576 ] / 2
=> x = [ 40 ± 24 ] / 2
=> x = 32 or x = 8
So, the two numbers are 32 and 8.
Difference between the two numbers = 32 - 8 = 24
Hence, the difference between the two numbers is 24.
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