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…
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?
30 years
32 years
34 years
36 years
Solution
Let father's age be X and son's age Y. From 'n years back I was as old as you are now': $X - n = Y$, so $X - Y = n$. From 'present age is four times your age n years back': $X = 4(Y - n)$. Substituting gives $5X = 8Y$, so $X = 8k$, $Y = 5k$. Since $X + Y = 130$, $13k = 130$, $k = 10$. Thus $X = 80$, $Y = 50$, and the difference is $80 - 50 = 30$ years.