The sum of the squares of three numbers is 532 and the ratio of the first and the second as also of the second and the third is 3 : 2. The third number is -

Answer: Option A

$$\begin{array}{rl}& \text{First}:\text{Second}=3:2,\\ & \text{Second}:\text{Third}=3:2\\ & =\left(3\times \frac{2}{3}\right):\left(2\times \frac{2}{3}\right)\\ & =2:\frac{4}{3}\\ & \therefore \text{Ratio between the numbers}\\ & =3:2:\frac{4}{3}\\ & =9:6:4.\end{array}$$
Let the numbers be 9x, 6x and 4x
Then,
= (9x)² + (6x)² + (4x)² = 532
⇒ 81x² + 36x² + 16x² = 532
⇒ 133x² = 532
⇒ x² = 4
⇒ x = 2
So, third number = 4x = 4 × 2 = 8