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?

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The correct answer is option A. 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.

Q29. 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?

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