The ratio of ages of a man and his son is 3 : 1. After 15 years, the age ratio will be 2 : 1. What is the age of the man?
45 years
40 years
35 years
30 years
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CAPF – 2018
Let the current age of the man be M years and the current age of the son be S years. The given ratio of their ages is M : S = 3 : 1, which can be written as M = 3S. After 15 years, the man’s age will be M + 15 and the son’s age will be S + 15. The new ratio of their ages is given as (M + 15) : (S + 15) = 2 : 1. This can be written as the equation (M + 15) / (S + 15) = 2. Cross-multiplying gives M + 15 = 2(S + 15), which simplifies to M + 15 = 2S + 30. Now substitute M = 3S into this equation: 3S + 15 = 2S + 30. Subtracting 2S from both sides gives S + 15 = 30. Subtracting 15 from both sides gives S = 15. The son’s current age is 15 years. The man’s current age is M = 3S = 3 * 15 = 45 years. To verify, after 15 years, the man will be 45 + 15 = 60 years old, and the son will be 15 + 15 = 30 years old. The ratio 60:30 simplifies to 2:1, which matches the condition given in the problem.
Set up algebraic equations based on the given ratios and conditions at different time points. Solve the system of equations to find the unknown ages.