Multiple Choice Questions on A father said to his son quot n years back I was as old as you are now My present age is four t........... for Civil Services Exam (CSAT) Preparation

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    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)
    30 years
    Correct Answer

    32 years

    Incorrect Answer

    34 years

    Incorrect Answer

    36 years

    Incorrect Answer
    Explanation:

    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.


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