Three numbers are in the ratio of 3 : 2 : 5 and the sum

Three numbers are in the ratio of 3 : 2 : 5 and the sum of their squares is 1862. The smallest of these numbers is

Let the numbers be 3x, 2x
and 5x respectively.
Now, (3x)² + (2x)² + (5x)²
= 1862
⇒ 9x² + 4x² + 25x² = 1862
⇒ 38x² = 1862

⇒ x² =	1862	= 49
	38

⇒ x = √49 = 7
∴ The smallest number
= 2x = 2 × 7 = 14