Question

The sum of two numbers is 45. If 5 is subtracted from each of them, the product of these numbers becomes 124. Find the numbers.

Answer 1

Let two numbers of x and y

According to the question,

x + y = 45

⇒ y = 45 – x  ...(i)

And (x – 5) (y – 5) = 124

⇒ (x – 5) [(45 – x) – 5] = 124  ...[From equation (i)]

⇒ (x – 5) (40 – x) = 124

⇒ 40x – 200 – x² + 5x = 124

⇒ x² – 45x + 324 = 0

⇒ x² – 36x – 9x + 324 = 0

⇒ x (x – 36) – 9 (x – 36) = 0

⇒ (x – 36) (x – 9) = 0

⇒ x – 36 = 0 or x – 9 = 0

⇒ x = 36 or x = 9

Now from equation (i),

When x = 36, then y = 45 – 36 = 9

When x = 9, then y = 45 – 9 = 36

Hence, the numbers are 9 and 36.