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Problems on Age
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Example 1: 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, one year ago, son's age be x years.
Then, man's age one year ago = 8x years.
Present age of son = (x + 1) years and,
Present age of man = (8x + 1) years.
(8x + 1) = (x + 1)2 [Given]
x2 - 6x = 0
x(x - 6) = 0
x = 0 or x = 6
x = 6 [Son's age cannot be 0]
Present age of son = (x + 1) years = 7 years.
and, Present age of man = (8x + 1) years = 49 years.

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Example 2: The product of Ramu's age (in years) five years ago with his age (in years) 9 years later is 15. Find Ramu's present age.
Solution: assume Ramu's present age be x years. Then,
His age 5 years ago = (x - 5) years.
His age 9 years later = (x + 9) years. 
the product of these ages is 15.(given)
 (x - 5)(x + 9) = 15
x2 + 4x - 60 = 0
x2 +10x - 6x - 60 = 0
(x + 10)(x - 6) = 0
x = 6 or, x = -10.
But, x -10. So,x = 6.
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