Question

Two numbers are in the ratio 2:3 and the difference of their squares is 320 the numbers are

Answer 1

Condition 1: a/b = 3/2, or a=1.5*b

Condition 2: a^2 - b^2 = 320

a = 1.5*b, then (1.5b)^2 - b^2 = 320

(2.25 - 1)*b^2 = 320

b^2 = 320/1.25 = 256

b = 16

a = 1.5*b = 24

the numbers are 24 and 16.

Answer 2

Let common ratio be x
Therefore, 1 number = 2x, other = 3x.
9x²-4x²=320 {given}
x²=320/5
x²=64
Therefore, x= √64 = 8
Therefore, Numbers are :
16 and 24