A number is multiplied by 11 and 11 is added to the product. If the resulting number is divisible by 13, the smallest original number is = ?

Answer: Option A

Let the required number be x.
Then, $$\frac{11x+11}{13}$$   = a whole number.
So, (11x + 11) must be divisible by 13
By hit and trial, we get x = 12
Hence, the smallest original number is 12