QUESTION

CSAT

Easy

Maths

Prelims 2024

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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Explanation

Let the father's age be $X$ and the son's age be $Y$ .
According to the problem:
- Equation 1: $X - Y = n$ .
- Equation 2: $X = 4(Y - n)$ .
Substitute $n$ from Equation 1 into Equation 2:
- Rearrange to get $X - Y = (4Y - X) \div 4$ .
- Simplify to find the ratio $X \div Y = 8 \div 5$ .
Assume $X = 8k$ and $Y = 5k$ .
Since $X + Y = 130$ :
- $8k + 5k = 130$ ,
- $13k = 130$ ,
- $k = 10$ .
Therefore:
- Father's age $X = 8k = 80$ years,
- Son's age $Y = 5k = 50$ years,
- Difference in age = $80 - 50 = 30$ years.