The average expense per boarder is Rs. 700 when there are 25 boarders.
Total cost for 25 boarders =700*25 =17500
The average expense per boarder is Rs. 600 when there are 50 boarders
Total cost for 50 boarders =600*50 =30000
Increment in cost when we add 25 boarders = 30000-17500 = 12500
The average cost per boarder when we add 25 boarders = $\frac{12500}{25} =500$
Total cost for 100 boarders = Total cost for 50 boarders + 2* The average cost per boarder when we add 25 boarders
=30000+25000
=55000
Thus,average expense per boarder for 100 boarders =$\frac{55000}{100} =550$
Hence,Option(A) 550 is the Answer.