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?

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? Correct Answer Rs. 550

Let the fixed cost be Rs. x and the variable cost be Rs. y per boarder.
Then,
x + 25y = 700 × 25
⇒ x + 25y = 17500.....(i)
x + 50y = 600 × 50
⇒ x + 50y = 30000.....(ii)
Subtracting (i) from (ii), we get:
25y = 12500
⇒ y = 500
Putting y = 500 in (i), we get:
x = 5000
∴ Total expenses of 100 boarders
= Rs. (5000 + 500 × 100)
= Rs. 55000
Hence, average expense
= Rs. $$\frac{55000}{100}$$
= Rs. 550