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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 ₹700 when there are 25 boarders and ₹600 - Mathematics

MCQ

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

Options

  • ₹550

  • ₹580

  • ₹540

  • ₹570

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Solution

₹550

Explanation:

Let x be fixed and y be the variable expense

average expense 25 boarders = 700

Total expense = 700 × 25 = 17500

average expense for 50 boarders = 600

Total expense = 600 × 50 = 30000

ATQ

x + 50y = 30,000

x + 25y = 17,500

By solving

25 y  = 12,500 = 500

x = 30000 − 25000

x = 5000

For 100 expense boarders

Total = 5000 + 100 × 500 = 5000 + 50000 = 55000

Average `=55000/100=550`

Concept: Number System (Entrance Exam)
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