#### 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

x^{2} + 8x - 5x - 40 = 30

x^{2} + 3x - 40 - 30 = 0

x^{2} + 3x - 70 = 0

x^{2} - 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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#### APPEARS IN

Solution 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. Concept: Solutions of Quadratic Equations by Factorization.