#### Question

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

#### Solution

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.

Is there an error in this question or solution?

Solution Two Positive Numbers Are in the Ratio 3 : 5 and the Difference Between Their Squares is 400. Find the Numbers. Concept: Ratios.