Question

The ratio of two numbers is 3:2 and the difference of their square is 500. Find the numbers.

Answer 1

Given: Ratio of two numbers = 3:2

So, let the two numbers be 3x and 2x.

Now, according to the question,

(3x)² – (2x)² = 500

⇒ 9x² – 4x² = 500

⇒ 5x² = 500

⇒ x² = `500/5` = 100

⇒ x = `sqrt(100)`

⇒ x = ± 10

For x = – 10,

First number = 3 × (– 10) = – 30

and second number = 2 × (–10) = – 20

For x = 10,

First number = 3 × (10) = 30

and second number = 2 × (10) = 20

Hence, the numbers are – 30, – 20 or 30, 20.