Question

CSATEasyPrelims 2024Maths

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?

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.