How many three-digit numbers exist whose first and last digits add up to 9?

Correct option is A

Solution : A three-digit number can be represented as $ABC$, where AAA is the hundreds digit, BBB is the tens digit, and CCC is the units digit. The condition given is that the first digit (AAA) and the last digit (CCC) must sum up to 9.

1. Possible values for AAA (hundreds digit) are $1,2,3,...,9$, as AAA must be a non-zero digit in a three-digit number.
2. For each AAA, the corresponding CCC is calculated as $C=9-A$. Hence, valid pairs of AAA and CCC are:
   • $(1,8),(2,7),(3,6),(4,5),(5,4),(6,3),(7,2),(8,1),(9,0)$.
   • This gives 9 pairs of $(A,C)$.
3. The tens digit BBB can be any digit from 000 to 999 (10 choices for each pair $(A,C)$).

Thus, the total number of such three-digit numbers is:

9×10=90 

Final Answer : Thus the correct answer is option (A) 90