Question

Product of Pragati’s age 2 years ago and 3 years hence is 84. Find her present age. 

Answer 1

Let Pragati's present age be x years. 

Her age 2 years ago = x - 2 

Her age 3 years hence = x + 3 

Product of Pragati’s age 2 years ago and 3 years hence is 84. 

\[\left( x - 2 \right)\left( x + 3 \right) = 84\]

\[ \Rightarrow x^2 + x - 6 = 84\]

\[ \Rightarrow x^2 + x - 90 = 0\]

\[x = \frac{- b \pm \sqrt{b^2 - 4ac}}{2a}\]

\[ \Rightarrow x = \frac{- 1 \pm \sqrt{1^2 - 4 \times 1 \times \left( - 90 \right)}}{2}\]

\[ = \frac{- 1 \pm \sqrt{361}}{2}\]

\[x = \frac{- 1 - 19}{2} or \frac{- 1 + 19}{2}\]

\[ \Rightarrow x = - 10 \text{ or } 9\]

But age cannot be negative so, x = 9.

Thus, Pragati's present age is 9 years.

Answer 2

Let Pragati's present age be x years. 

Her age 2 years ago = x - 2 years

Her age 3 years hence = x + 3 years

According to the given condition,

(x - 2) (x + 3) = 84

x(x + 3) -2(x + 3) = 84

x² + 3x - 2x - 6 = 84 

x² + x - 6 - 84 = 0

x² + x - 90 = 0

x² + 10x - 9x - 90 = 0

x(x + 10) -9(x + 10) = 0

(x + 10) (x - 9) = 0

 x + 10 = 0 or x - 9 = 0

x = -10 or x = 9

But age cannot be negative

∴ Pragati's present age is 9 years.