If the 6-digit number N83M92 is divisible by 11, then which of the options below can give a possible correct relation between M and N?

Correct option is B

Given:

6-digit number: N 8 3 M 9 2

The number is divisible by 11.

Need the correct relation between M and N.

Concept Used:

Divisibility rule of 11: Sum of digits at odd positions - Sum of digits at even positions
must be 0 or a multiple of 11.

Solution:

Positions (from left):

1:N, 2:8, 3:3, 4:M, 5:9, 6:2

Odd-position sum = N + 3 + 9 = N + 12

Even-position sum = 8 + M + 2 = M + 10

Difference for divisibility by 11:

(N + 12) - (M + 10) = N - M + 2

Set equal to 0 (the simplest multiple of 11):

N - M + 2 = 0

M - N = 2

The required relation is:

M - N = 2