Two numbers are in the ratio of 8 : 3. If their sum is 11, then what is the sum of the squares of the two numbers?

Correct option is C

Given:

Two numbers are in the ratio 8 : 3
Their sum = 11
Find the sum of the squares of the two numbers

Solution:
Let the numbers be:

​$$8x \text{ and } 3x \\\text{Then, } 8x + 3x = 11 \Rightarrow 11x = 11 \Rightarrow x = 1\\[10pt]\text{So, the numbers are } 8 \times 1 = 8 \text{ and } 3 \times 1 = 3\\[10pt]\text{Sum of squares} = 8^2 + 3^2 = 64 + 9 = \boxed{73}$$

Final Answer: (C) 73​​