29. A father said to his son, “n years back I was as old as you are now. My present age is four times your age n years back”. If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages?

1. A. 30 years
2. B. 32 years
3. C. 34 years
4. D. 36 years

Answer: A

Explanation

Let the present age of the father be F and the present age of the son be S. From the first statement: ‘n years back I was as old as you are now.’ This translates to F – n = S, which implies F – S = n (Equation 1). From the second statement: ‘My present age is four times your age n years back.’ This translates to F = 4(S – n) (Equation 2). Substitute n from Equation 1 into Equation 2: F = 4(S – (F – S)) => F = 4(2S – F) => F = 8S – 4F => 5F = 8S. This gives the ratio F:S = 8:5. Let F = 8k and S = 5k for some constant k. From the third statement: ‘the sum of the present ages of the father and the son is 130 years.’ So, F + S = 130 => 8k + 5k = 130 => 13k = 130 => k = 10. Therefore, Father’s present age F = 8 × 10 = 80 years, and Son’s present age S = 5 × 10 = 50 years. The difference in their ages = F – S = 80 – 50 = 30 years. This question tests the ability to set up and solve linear equations based on age-related word problems.