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Question:

At a reputed Engineering College in India, total expenses of a trimester are partly fixed and partly varying linearly with the number of students. The average expense per student is Rs.400 when there are 20 students and Rs.300 when there are 40 students. When there are 80 students, what is the average expense per student?

Explanation:

Let the fixed expenses be k.

Let the variable expenses per student be m.

∴ $\frac{20 m + k}{20}$ = 400 ...(i)

$\frac{40 m + k}{40}$ = 300 ...(ii)

Solving (i) and (ii) simultaneously, we get m = 200 and k = 4000

There average cost for 80 students will be

= $\frac{80 \times 200 + 4000}{80}$ = Rs. 250.

Hence, option (a).

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