If the product of two numbers is 360 and their ratio is 10 : 9, then find the numbers.

Let a and b be two numbers.

Given that a:b = 10:9

Product of a and b = ab = 360

Let the first number ‘a’ = 10x

Then the second number ‘b’ = 9x

Consider ab = 360

⇒ 10x × 9x = 360

⇒ 90x² = 360

⇒ x² = 4

⇒ x = 2

If x = 2, then first number ‘a’ = 10x = 10 × 2 = 20

The second number ‘b’ = 9x = 9 × 2 = 18

If x = -2, then first number ‘a’ = 10x = 10 × (-2) = -20

The second number ‘b’ = 9x = 9 × (-2) = -18