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Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is Rs. 700 when there are 25 boarders and Rs. 600 when there are 50 boarders. What is the average expense per boarder when there are 100 boarders?

1. 550
2. 580
3. 540
4. 570

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 =$\frac{55000}{100} =550$

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