Show Answer Type Questions (SLAB-I)
One
year ago, a man was 8 times as old as his son.
Now his age is equal to the square of his son's age
find their present age.
Answers
Question : One year ago, a man was 8 times as old as his son.
Now his age is equal to the square of his son's age . Find their present ages !
Solution : Let the present age of the son be x years .
So, the age of the son one year ago is (X - 1) years .
The man's age is 8 times his son's age now.
Age of the man 1 year ago > 8(x - 1) years
Current age of man > 8(x - 1) + 1 years
> 8x - 8 + 1
> 8x - 7 years .
This is equal to the square of the son's age .
Therefore
> 8x - 7 = x²
> x² - 8x + 7 = 0
> x² - 7x - x + 7 = 0
> x( x - 7 ) + 1( x - 7) = 0
> ( x + 1)( x - 7) = 0
x = 7 or -1 .
However the age can never be in negative .
So, the only possible value of x is 7 .
Thus,
The current age of the man is 49 years .
The current age of his son is 7 years.
This is the required answer .
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