Question

Two positive numbers are in the ratio 3 : 5 and the difference between their squares is 400. Find the numbers.

Answer 1

Let the two numbers be 3x and 5x.
According to the given information

`(5x)^2 − (3x)^2 = 400`
`25x^2 − 9x^2 = 400`
`16x^2 = 400`
`x^2 = 25`
x = 5
Thus, the numbers are 3 × 5 = 15 and 5 × 5 = 25.