Question

Two numbers are in the ration 3 : 5. If the sum of their squares is 2176, find the sum of the two numbers.
1. 64
2. 68
3. 60
4. 56

Answer 1

Correct Answer - Option 1 : 64

Given:

The ratio of numbers = 3 ∶ 5

Sum of their squares = 2176

Calculation:

Let the numbers be 3x and 5x.

The squares of the numbers are 9x² and 25x² respectively.

Sum of squares = 9x2 + 25x2 = 2176

34x² = 2176 Or, x² = 64

Then, x = 8 

Sum of the numbers = 3x + 5x = 8x = 64

∴ The sum of the numbers is 64.