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 -

Solution(By Examveda Team)

$$\eqalign{ & {\text{First}}:{\text{Second}} = 3:2, \cr & {\text{Second}}:{\text{Third}} = 3:2 \cr & = \left( {3 \times \frac{2}{3}} \right):\left( {2 \times \frac{2}{3}} \right) \cr & = 2:\frac{4}{3} \cr & \therefore {\text{Ratio between the numbers}} \cr & = 3:2:\frac{4}{3} \cr & = 9:6:4. \cr} $$
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