Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:

Understanding the Question:
This question asks us to find the largest number (N) that divides three given numbers (1305, 4665, and 6905) and leaves the same remainder in each division.
After finding N, we need to calculate the sum of its digits.

Key Concept: Finding N
If a number 'N' leaves the same remainder 'R' when dividing numbers 'a', 'b', and 'c', then (a-b), (b-c), and (c-a) are perfectly divisible by N.
In other words, 'N' is the Highest Common Factor (HCF) of the differences between the numbers.

Steps to Solve:
1. Calculate the differences:
* 4665 - 1305 = 3360
* 6905 - 4665 = 2240
* 6905 - 1305 = 5600
2. Find the HCF of these differences (3360, 2240, and 5600): The HCF of these numbers is 1120.
Therefore, N = 1120
3. Calculate the sum of the digits of N:
* 1 + 1 + 2 + 0 = 4

Conclusion:
The sum of the digits in N is 4.
Therefore, the correct option is A: 4