Two positive numbers are in the ratio 3 : 5 and the difference between their squares is 400. Find the numbers.
Let the two numbers be 3x and 5x.
According to the given information
(5x)2 − (3x)2 = 400
25x2 − 9x2 = 400
16x2 = 400
x2 = 25
x = 5
Thus, the numbers are 3 × 5 = 15 and 5 × 5 = 25.
