Question

Tinu is younger than Pinky by three years. The product of their ages is 180. Find their ages.

Answer 1

Let Pinky’s age be x years. Then, Tinu’s age will be (x – 3) years.
Thus, by the given condition,
x(x – 3) = 180
$\Rightarrow$ x² – 3x = 180
$\Rightarrow$ x² – 3x – 180 = 0
On splitting the middle term –3x as 12x – 15x, we get:
x² + 12x – 15x – 180 = 0
$\Rightarrow$ x(x + 12) – 15(x + 12) = 0
$\Rightarrow$ (x + 12)(x – 15) = 0
$\Rightarrow$ x + 12 = 0 or x – 15 = 0
$\Rightarrow$ x = –12 or x = 15
Since, age cannot be negative, x = 15
Thus, Pinky’s age is 15 years and Tinu’s age is (x – 3 =) 12 years.