If the ratio of two numbers is 1 : 5 and their product is

If the ratio of two numbers is 1 : 5 and their product is 320, then the difference between the squares of these two numbers is :

Let the numbers be x and 5x.
According to the question,
x × 5x = 320
⇒ 5x² = 320

⇒ x² =	320	= 64
	5

⇒ x = √64 = 8
∴ Required difference
= (5x)² – x²
= 25x² – x² = 24x²
= 24 × 8 × 8 = 1536