Given:
- The total expenses of running the hostel at IIM Ahmedabad are partly fixed and partly varying linearly with the number of boarders.
- The average expense per boarder is Rs.70 when there are 25 borders.
- The average expense per boarder is Rs.60 when there are 50 boarders.
- We need to find the average expense per boarder when there are 100 boarders.

Let's assume that the total expenses of running the hostel can be represented as:
Total expenses = Fixed expenses + Variable expenses

We can also assume that the variable expenses are proportional to the number of boarders:
Variable expenses = k * number of boarders

where k is a constant of proportionality.

Using the given information, we can form two equations:
1. When there are 25 boarders:
Total expenses = Fixed expenses + k * 25
Average expense per boarder = Total expenses / 25 = Rs.70
Solving for Fixed expenses and k, we get:
Fixed expenses = Rs. 350
k = Rs. 8

2. When there are 50 boarders:
Total expenses = Fixed expenses + k * 50
Average expense per boarder = Total expenses / 50 = Rs.60
Substituting the values of Fixed expenses and k, we get:
Total expenses = Rs. 750
Therefore, Fixed expenses + k * 50 = Rs. 750
Solving for Fixed expenses and k, we get:
Fixed expenses = Rs. 100
k = Rs. 13

Now, we can use the value of k to find the total expenses when there are 100 boarders:
Total expenses = Fixed expenses + k * 100
Total expenses = Rs. 100 + Rs. 13 * 100 = Rs. 1400

Therefore, the average expense per boarder when there are 100 boarders is:
Average expense per boarder = Total expenses / 100 = Rs. 14

Hence, the correct option is (a) 55.