The product of Shikha’s age five years ago and her age 8 years later

1.	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.
Answer» Let’s assume the present age of Shikha be x years So, 8 years later, age of her = (x + 8) years Five years ago, her age = (x – 5) years Given relationship between the ages can be expressed as: (x – 5)(x +8) = 30 x²+ 8x – 5x – 40 = 30 x² + 3x – 40 – 30 = 0 x²+ 3x – 70 = 0 [By factorisation method] x(x – 7) + 10(x – 7) = 0 (x – 7)(x + 10) = 0 x = 7 or x = -10 (neglected) Since, the age can never be negative. Therefore, the present age of Shikha is 7 years.

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.

Answer»

Let’s assume the present age of Shikha be x years

So, 8 years later, age of her = (x + 8) years

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

Given relationship between the ages can be expressed as:

(x – 5)(x +8) = 30

x²+ 8x – 5x – 40 = 30

x² + 3x – 40 – 30 = 0

x²+ 3x – 70 = 0 [By factorisation method]

x(x – 7) + 10(x – 7) = 0

(x – 7)(x + 10) = 0

x = 7 or x = -10 (neglected)

Since, the age can never be negative.

Therefore, the present age of Shikha is 7 years.