Question

A two-digit number is such that the product of the digits is 16. When 54 is subtracted from the number, the digits are interchanged. Find 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 16. 

⇒ ab = 16 --- (1) 

Also, when 54 is subtracted from the number, the digits interchange their places 

⇒ 10b + a – 54 = 10a + b 

⇒ 9b – 9a = 54 

⇒ b – a = 6 

⇒ b = 6 + a 

Substituting in 1 

⇒ a × (6 + a) = 16 

⇒ a² + 6a – 16 = 0 

⇒ a² + 8a – 2a – 16 = 0 

⇒ a(a + 8) – 2(a + 8) = 0 

⇒ (a – 2)(a + 8) = 0 

⇒ a = 2 

Thus, b = 8 

Number is 82