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# The Product of Ramu'S Age (In Years) Five Years Ago and His Age (In Years) Nice Years Later is 15. Determine Ramu'S Present Age. - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### Question

The product of Ramu's age (in years) five years ago and his age (in years) nice years later is 15. Determine Ramu's present age.

#### Solution

Let the present age of Ramu be x years

Then, 9 years later, age of her = (x + 9) years

Five years ago, her age = (x - 5) years

Then according to question,

(x - 5)(x + 9) = 15

x2 + 9x - 5x - 45 = 15

x2 + 4x - 45 - 15 = 0

x2 + 4x - 60 = 0

x2 - 6x + 10x - 60 = 0

x(x - 6) + 10(x - 6) = 0

(x - 6)(x + 10) = 0

So, either

x - 6 = 0

x = 6

Or

x + 10 = 0

x = -10

But the age never be negative

Hence, the present age of Ramu be 6 years.

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Solution The Product of Ramu'S Age (In Years) Five Years Ago and His Age (In Years) Nice Years Later is 15. Determine Ramu'S Present Age. Concept: Solutions of Quadratic Equations by Factorization.
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