Question

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.

Answer 1

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