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Question
The product of Shikha's age five years ago and her age 8 years later is 30, her age at both times being given in years. Find her present age.
Solution
Let the present age of Shikha be x years
Then, 8 years later, age of her = (x + 8) years
Five years ago, her age = (x - 5) years
Then according to question,
(x - 5)(x + 8) = 30
x2 + 8x - 5x - 40 = 30
x2 + 3x - 40 - 30 = 0
x2 + 3x - 70 = 0
x2 - 7x + 10x - 70 = 0
x(x - 7) + 10(x - 7) = 0
(x - 7)(x + 10) = 0
So, either
x- 7 = 0
x = 7
Or
x + 10 = 0
x = -10
But the age never be negative
Hence, the present age of Shikha be 7 years.
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