The missing digit is represented by A ⇒ $1A2, where A represents a whole number from 0 to 9.
Try substituting any number from 0 to 9 for A (the middle digit or tens place) , then divide by 11 members.
Option 1: A = 2 ⇒ $1 2 2
$122 ÷ 11 = $11.09090909...
Option 2: A = 3 ⇒ $1 3 2
$ 132 ÷ 11 = $12
Option 3: A = 9 ⇒ $ 1 9 2
$ 192 ÷ 11 = $ 17,45454545,,,
When you substitute the rest of the one-digit number for A, the decimals are repeating. (Amazing, right? Try it)
The only one-digit that gives a whole number quotient when it takes the place of tens digit in $1 __2 is 3. Because $ 132 ÷ 11 = $ 12. (Option 2)
The missing digit is 3.