Question -
Answer -
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 10and 40.