Question

Given a  + b = a,b∈ R⁺ 50 . If A, G and H are, respectively, the AM, GM and HM between the numbers a and b, such that the GM exceeds HM by 4, then (where A >1, G > 1, H > 1)

(A)   A + G = 30 H

(B)  G + H = A + 11

(C)  4 (G + H) = A − 1

(D)  A + G = 3(H − 1)

Answer 1

Correct option  (B), (D)

a + b = 50

Hence, A = 25, G

Hence, H = 16 or 1

Since H > 1, hence H = 16

But since G₂ = AH, hence

G = 20, H = 16 is the only possibility.