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.