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?
This questions was previously asked in
UPSC CSAT, Previous year (2024)
32 years
Incorrect Answer34 years
Incorrect Answer36 years
Incorrect AnswerExplanation:
Let's break it down:
- Let son’s present age = x years, father’s present age = y years.
- "n years back, I was as old as you are now" ? y - n = x
- "My present age is four times your age n years back" ? y = 4(x - n)
- The sum of their ages: x + y = 130
From (1): y - n = x ? n = y - x
Substitute n into (2):
y = 4(x - (y - x)) = 4(2x - y)
So, y = 8x - 4y ? 5y = 8x ? y = (8/5)x
Now use x + y = 130
x + (8/5)x = 130 ? (13/5)x = 130, x = 50, y = 80
Difference = 80 - 50 = 30 years
So, option 1 ("30 years") is correct.
By: Parvesh Mehta ProfileResourcesReport error