Consider the number `N = 8 7 a 2 7 9 3 1 b`, where b is digit at unit's place and a is a digit at ten lac place. Answer the following questions.
The greatest value of b which N is divisible by 8 is

Options

A. `0`
B. `2`
C. `4`
D. `6`

Explanation

To determine the greatest value of \( b \) such that the number \( N = 87A27931B \) is divisible by 8, we need to apply the divisibility rule for 8. According to this rule, a number is divisible by 8 if the number formed by its last three digits is divisible by 8.

### Step-by-Step Solution:

1. **Identify the last three digits**: The last three digits of the number \( N \) are \( 31B \), where \( B \) is the digit at the unit's place.

2. **Form the number with \( B \)**: The last three digits can be expressed as \( 31B \). This means we can represent it as \( 310 + B \).

3. **Check divisibility by 8**: We need to find values of \( B \) (where \( B \) can be any digit from 0 to 9) such that \( 310 + B \) is divisible by 8.

4. **Calculate \( 310 \mod 8 \)**:
\[ 310 \div 8 = 38.75 \quad \text{(the integer part is 38)} \]
\[ 38 \times 8 = 304 \]
\[ 310 - 304 = 6 \]
Thus, \( 310 \equiv 6 \mod 8 \).

5. **Set up the equation for divisibility**: We need \( 310 + B \equiv 0 \mod 8 \). Since \( 310 \equiv 6 \mod 8 \), we have:
\[ 6 + B \equiv 0 \mod 8 \]
This simplifies to:
\[ B \equiv -6 \mod 8 \quad \text{or} \quad B \equiv 2 \mod 8 \]

6. **Find possible values for \( B \)**: The possible values of \( B \) that satisfy \( B \equiv 2 \mod 8 \) within the range of digits (0-9) are:
- \( B = 2 \)
- \( B = 10 \) (not a valid digit)

Therefore, the only valid digit for \( B \) is \( 2 \).

7. **Conclusion**: The greatest value of \( B \) such that \( N \) is divisible by 8 is \( 2 \).

### Final Answer:
The greatest value of \( b \) which \( N \) is divisible by 8 is \( \boxed{2} \).