Question

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

Answer 1

Hint: We had to only find the smallest 9-digit number and the greatest 8-digit number that can be formed using digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. And then find the sum of the both numbers.

Complete Step-by-Step solution:
Now as we know that the n-digit number has a total number of digits equal to n.
And each and every number is made from the digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. And the greatest digit in this set is 9 and the smallest digit in the set is 0.
So, if we are asked to find the greatest n-digits number then all the digits of the number must be 9 because 9 is the greatest digit at all.
So, the greatest 8-digit number will be the number which has 8-digits and all digits must be equal to 8.
Hence, the greatest 8-digit number will be 9,99,99,999
Now we had to find the smallest 9-digits number.
As we know the smallest digit is zero. But if the first digit of any number is zero then the number of digits of the number will be decreased by one. So, the first digit of a smallest n-digits number should be the second smallest digit (i.e. 1). And all other digits must be equal to zero.
So, the smallest 9-digits number must have 9-digits and all digits except the first digit must be equal to 0 and the first digit must be equal to 1.
Hence, the smallest 9-digits number will be 10,00,00,000
So, now we had to find the sum of the greatest 8-digit number and smallest 9-digit number.
So, 9,99,99,999 + 10,00,00,000 = 19,99,99,999
Hence, the correct option will be B.

Note: Whenever we come up with this type of problem then we should remember that the smallest digit that can be used to form a number is zero. But the first digit of any number cannot be zero because if the first digit is zero then the total number of a digits in the number will be decreased by one. So, if we are asked to find the smallest n-digits number then its first digit must be 1 and all other digits should be equal to 0 because 1 is the second smallest digit after zero.