Answer (Detailed Solution Below)
Option 2 : 6 and 3
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120 Qs. 480 Marks 120 Mins
Concept:
Let x and y be the two numbers. The the arithmetic mean A, geometric mean G and the harmonic mean H of x and y is given by,
⇒ A =
⇒ G2 = xy
⇒
Calculations:
Consider, the two numbers are x and y.
Given, the arithmetic mean and geometric mean of the x and y is A and G.
⇒ A = ....(1)
⇒ G2 = xy ....(2)
The harmonic mean of two number x and y is 4.
⇒
⇒ 2xy = 4(x + y)
⇒
⇒ G2 = 4A (∵ x + y = 2A)
⇒ G2 = 4A ....(3)
Given, Their arithmetic mean A and the geometric mean G satisfy the relation 2A + G2 = 27.
⇒2A + G2 = 27
⇒ 6A = 27
⇒ A =
From equation (1), (2) and (3), we have
x + y = 9 and xy = 18
⇒ x = 6 and y = 3
Hence, the harmonic mean of two number is 4, Their arithmetic mean A and the geometric mean G satisfy the relation 2A + G2 = 27, then the two numbers are 6 and 3.
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If AM and GM of two positive numbers a and b are 10 and 8 respectively, find the numbers.
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