Five digit numbers are formed such that either all the digits are even or all the digits are odd. If no digit is allowed to be repeated in one number find the difference between the maximum possible. number with odd-digits and the minimum possible number with even digits

Options

A. 77063
B. 79999
C. 72841
D. 86420

Answer

To solve the problem, we need to find the maximum possible five-digit number using odd digits and the minimum possible five-digit number using even digits, and then calculate the difference between these two numbers.

### Step-by-Step Solution:

1. **Identify Odd Digits**: The odd digits available are 1, 3, 5, 7, and 9.

2. **Form the Maximum Odd Number**: To form the maximum five-digit number using odd digits, we arrange the digits in descending order:
- The digits in descending order are: 9, 7, 5, 3, 1.
- Therefore, the maximum five-digit number with odd digits is **97531**.

3. **Identify Even Digits**: The even digits available are 0, 2, 4, 6, and 8.

4. **Form the Minimum Even Number**: To form the minimum five-digit number using even digits, we must ensure that the first digit is not zero (as it cannot be a leading digit in a five-digit number). Thus, we start with the smallest non-zero even digit:
- The smallest non-zero even digit is 2. The remaining digits in ascending order are 0, 4, 6, and 8.
- Therefore, the digits in ascending order starting with 2 are: 2, 0, 4, 6, 8.
- The minimum five-digit number with even digits is **20468**.

5. **Calculate the Difference**: Now, we find the difference between the maximum odd number and the minimum even number:
- Maximum odd number = 97531
- Minimum even number = 20468
- Difference = 97531 - 20468

Let's perform the subtraction:
```
97531
-20468
-------
77063
```

6. **Final Result**: The difference between the maximum possible number with odd digits and the minimum possible number with even digits is **77063**.

### Summary:
The required difference is **77063**.