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

1.	Product of Pragati’s age 2 years ago and years hence is 84. Find her present age.
Answer» Let the present age of Pragati be x years. ∴ 2 years ago, Age of Pragati = (x – 2) years After 3 years, Age of Pragati = (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 By using the property, if the product of two numbers is zero, then at least one of them is zero, we get ∴ x + 10 = 0 or x – 9 = 0 ∴ x = -10 or x = 9 But, age cannot be negative. ∴ x = 9 ∴ Present age of Pragati is 9 years.

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

Answer»

Let the present age of Pragati be x years.

∴ 2 years ago,

Age of Pragati = (x – 2) years

After 3 years,

Age of Pragati = (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

By using the property, if the product of two numbers is zero, then at least one of them is zero, we get

∴ x + 10 = 0 or x – 9 = 0

∴ x = -10 or x = 9 But, age cannot be negative.

∴ x = 9

∴ Present age of Pragati is 9 years.