Question

Find the two numbers whose A.M. is 25 and GM is 20.

Answer 1

Given: A.M = 25, G.M = 20.

G.M = √ab

A.M = (a + b)/2

So,

√ab = 20 ……. (1)

(a + b)/2 = 25……. (2)

a + b = 50

a = 50 – b

Putting the value of ‘a’ in equation (1), we get,

√[(50 - b)b] = 20
50b – b² = 400

b² – 50b + 400 = 0

b² – 40b – 10b + 400 = 0

b(b – 40) – 10(b – 40) = 0

b = 40 or b = 10

If b = 40 then a = 10

If b = 10 then a = 40

∴ The numbers are 10 and 40.