Explanation:

- We start with an average (mean) of five numbers, which is 45.

- The sum of these five numbers is $5\times 45=225$.

- Adding a sixth number changes the average to 48.

- The new total for six numbers is $6\times 48=288$.

- The sixth number equals the new total minus the original total: $288-225=63$.

- Option 1: 73 - This would make the total 298, not 288.

- Option 2: 63 - This makes the total 288, which matches.

- Option 3: 43 - Too low; the total would be 268.

- Option 4: 53 - The total would be 278; still too low.