CSAT 2024

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.

More Questions:
UPSC Factory App
Get everything you need for upsc preparation with just one click! Install now!