# 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?

a) 30 years

b) 32 years

c) 34 years

d) 36 years

Correct answer: a) 30 years

#### Question from UPSC Prelims 2024 CSAT

**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.