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A boy finds the average of $10$ positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say $ba$ for $ab.$ Due to this, the average becomes $1.8$ less than the previous one. What is the difference between two digits $a$ and $b?$

  1. $4$
  2. $2$
  3. $6$
  4. $8$
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