abcde is a five digit number when multiplied by 13 it gives a number, purely formed by the digit 9. Then the value of `a + b + c + d + e` is :

Options

A. divisible by 8
B. equal to 27
C. divisible by 11
D. all of these

Answer

To solve the problem, we need to find a five-digit number \( abcde \) such that when it is multiplied by 13, the result is a number composed entirely of the digit 9. The number formed by the digit 9 can be represented as \( 999999 \).

### Step-by-Step Solution:

1. **Understand the problem**: We need to find a five-digit number \( abcde \) such that:
\[ abcde \times 13 = 999999 \]

2. **Divide 999999 by 13**: To find \( abcde \), we can rearrange the equation:
\[ abcde = \frac{999999}{13} \]

3. **Perform the division**: Now, we calculate \( 999999 \div 13 \):
- Performing the division:
\[ 999999 \div 13 = 76923 \]

4. **Verify that \( 76923 \) is a five-digit number**: The result \( 76923 \) is indeed a five-digit number.

5. **Identify the digits**: The digits \( a, b, c, d, e \) correspond to:
- \( a = 7 \)
- \( b = 6 \)
- \( c = 9 \)
- \( d = 2 \)
- \( e = 3 \)

6. **Calculate the sum of the digits**: Now, we need to find \( a + b + c + d + e \):
\[ a + b + c + d + e = 7 + 6 + 9 + 2 + 3 \]

7. **Perform the addition**:
- First, add \( 7 + 6 = 13 \)
- Then, \( 13 + 9 = 22 \)
- Next, \( 22 + 2 = 24 \)
- Finally, \( 24 + 3 = 27 \)

8. **Final result**: Thus, the value of \( a + b + c + d + e \) is:
\[ \boxed{27} \]