The difference between two numbers is 8. If 2 is added to the bigger number the result will be three times the smaller number. Find the numbers.

Let the smaller number be x.

The difference between the two numbers = 8.

∴ The bigger number = x + 8.

According to the given condition,

(x + 8) + 2 = 3x

⇒ x + 8 + 2 = 3x

x + 10 = 3x

⇒ 10 = 3x – x (Transposing x to RHS)

10 = 2x

⇒ = x (Transposing 2 to LHS)

5 = x

∴ x = 5

The smaller number = x = 5

The bigger number = x + 8 = 5 + 8 = 13

∴ The two numbers are 5 and 13.