text: Share
  
  # A Two-digit Number is Such that the Products of Its Digits is 8. When 18 is Subtracted from the Number, the Digits Interchange Their Places. Find the Number? - Mathematics
  
  Course
  
  #### Question
  
  A two-digit number is such that the products of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number?
  
  #### Solution
  
  Let the two digits be x and x - 2
  
  Given that the product of their digits is 8.
  
  ⇒ x(x - 2) = 8
  
  ⇒ 𝑥2 - 2𝑥 - 8 = 0
  
  ⇒ 𝑥2 - 4𝑥 + 2𝑥 - 8 = 0
  
  ⇒ 𝑥(𝑥 - 4) + 2(𝑥 - 4) = 0
  
  ⇒ (𝑥 - 4)(𝑥 + 2) = 0
  
  ⇒ 𝑥 = 4 𝑜𝑟 𝑥 = -2
  
  Considering the positive value x = 4, x - 2 = 2.
  
  ∴ The two digit number is 42.
  
  Is there an error in this question or solution?