Question

7) The product of Amar's age (in years), five years ago, with his age 9 years later, is 15.
Find Amar's present age.​

Answer 1

Working out:

In this question, we have to work with only one variable for Amar's age, and then predicting the age 5 years ago, and 9 years later. The product is given, from here we can frame a equation to solve for Aman's age.

Let,

Present age of Amar be x

Then,

• Age of Amar 5 years ago = x - 5
• Age of Amar 9 years later = x + 9

According to question,

➝ Product of age 5 years ago and 9 years later = 15

➝ (x - 5)(x + 9) = 15

Opening the parentheses,

➝ x(x + 9) - 5(x + 9) = 15

➝ x² + 9x - 5x - 45 = 15

➝ x² + 4x - 45 = 15

➝ x² + 4x - 45 - 15 = 0

➝ x² + 4x - 60 = 0

Factorising by middle term factorsation,

➝ x² + 10x - 6x - 60 = 0

➝ x(x + 10) - 6(x + 10) = 0

➝ (x + 10)(x - 6) = 0

Then, x = -10 or 6

Age can't be in negative, so x = 6 is the possible value.

Hence, present age of Amar:

$\large{ \boxed{ \bf{ \red{6 \: years}}}}$

Quick check:

• Age of Amar 5 years ago = 6 - 5 = 1
• Age of Amar 9 years later = 6 + 9 = 15

Product = 1 × 15 = 15✓

And, we are done !!

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Answer 2

SOLUTION :

LET THE AGE OF AMAR= x

According to the question,

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

$= > x {}^{2} \: + 9x - 5x - 45 - 15 = 0$

$= > x {}^{2} + 4x - 60 = 0$

$= > x {}^{2} + 10x - 6x - 60 = 0(by \: factorise)$

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

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

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

=> x = -10 (or) x = 6

=> AGE CANNOT BE NEGATIVE.

THEREFORE THE AGE OF AMAR = 6

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