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Sum of the greatest 8-digit number and the smallest 9-digit number is
$
  {\text{A}}{\text{. 1,99,99,999}} \\
  {\text{B}}{\text{. 19,99,99,999}} \\
  {\text{C}}{\text{. }}99,99,99,999 \\
  {\text{D}}{\text{. }}1,00,00,999 \\
$

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Answer
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Hint: In this question we need firstly to find the greatest 8-digit number and the smallest 9-digit number. Then after finding them we will add those numbers. Using this we would be able to get our answer.

Complete step-by-step answer:

The greatest 8-digit number is 9,99,99,999 and the smallest 9-digit number is 10,00,00,000.
So, the sum of the greatest 8-digit number and the smallest 9-digit number is,
10,00,00,000 + 9,99,99,999 = 19,99,99,999
Hence, option B is correct.

Note: Whenever we face such types of problems the value point to remember is that we need to have a good grasp over number theory and simple addition and subtraction. We must also know how to find the greatest and smallest numbers of a particular length. This helps in getting us the required expressions and gets us on the right track to reach the answer.