A two-digit number is such that the product of the digits is 12. When 36 is added to the number the digits interchange their places. Determine the number.

Let the ones digit be ‘a’ and tens digit be ‘b’.

Given, two-digit number is such that the product of its digits is 12.

⇒ ab = 12 --- (1)

Also, when 36 is added to the number, the digits interchange their places

⇒ 10b + a + 36 = 10a + b

⇒ 9a – 9b = 36

⇒ a – b = 4

⇒ a = 4 + b

Substituting in 1

⇒ b × (4 + b) = 12

⇒ b² + 4b – 12 = 0

⇒ b² + 6b – 2b – 12 = 0

⇒ b(b + 6) – 2(b + 6) = 0

⇒ (b – 2)(b + 4) = 0

⇒ b = 2

Thus, a = 6

Number is 26