If 5 times a son's age is added to his father's age, the sum is 42 years. If 2.8 times the father's age is added to the son's age, the sum is 76 years. What is the father's age (in years)?

Correct option is D

​$$\textbf{Given:} \\\text{Let the son's age} = x \text{ years} \\\text{Let the father's age} = y \text{ years}\\\textbf{According to the question:} \\5 \times (\text{son's age}) + (\text{father's age}) = 42 \\\Rightarrow 5x + y = 42 \quad \text{...(1)}2.8 \times (\text{father's age}) + (\text{son's age}) = 76 \\\Rightarrow x + 2.8y = 76 \quad \text{...(2)}\\\textbf{Formula Used:} \\\text{Solution of simultaneous linear equations}\\\textbf{Solution:} \\\text{From equation (1):} \\y = 42 - 5x\text{Substitute } y \text{ in equation (2):} \\x + 2.8(42 - 5x) = 76 \\x + 117.6 - 14x = 76 \\-13x = 76 - 117.6 \\-13x = -41.6 \\x = 3.2\text{Now find the father's age:} \\y = 42 - 5(3.2) \\y = 42 - 16 \\y = 26\\\textbf{Father's age} = 26 \text{ years}$$​​