Q. 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 : 

Father Son Age Problem

Let’s approach this step-by-step:

1. Let’s define some variables:
F = Father’s present age
S = Son’s present age
n = Number of years mentioned in the problem

2. From the given information:
F – n = S (Father’s age n years ago was equal to son’s present age)
F = 4(S – n) (Father’s present age is 4 times son’s age n years ago)

3. We’re also told that the sum of their present ages is 130:
F + S = 130

4. Let’s solve the equations:
From the first equation: S = F – n
Substituting this into the second equation:
F = 4(F – n – n) = 4F – 8n

3F = 8n
F = 8n/3

5. Now, let’s use the third equation:
F + S = 130
(8n/3) + (8n/3 – n) = 130
16n/3 – n = 130
16n/3 – 3n/3 = 130
13n/3 = 130
13n = 390
n = 30

6. Now that we know n, we can find F and S:
F = 8n/3 = 8(30)/3 = 80
S = F – n = 80 – 30 = 50

7. The difference in their ages is:
80 – 50 = 30

Therefore, the difference in their ages is 30 years.

The correct answer is a) 30 years.