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?
Show Hint
- 540
- 580
- 550
- 560
The Correct Option is C
Solution and Explanation
Let total expense \( = F + vN \) (F fixed, v variable cost per boarder). Average per boarder \( = \dfrac{F}{N} + v \).
Step 2: Two equations.
\( \dfrac{F}{25} + v = 700 \) and \( \dfrac{F}{50} + v = 600 \).
Subtracting: \( \dfrac{F}{25} - \dfrac{F}{50} = 100 \Rightarrow \dfrac{F}{50} = 100 \Rightarrow F = 5000 \). Then \( v = 600 - 100 = 500 \).
Step 3: For 100 boarders.
Average \( = \dfrac{5000}{100} + 500 = 50 + 500 = 550 \).
Final Answer:
The correct option is (3): Rs. 550
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