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Question

# 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?

A
Rs. 550
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B
Rs. 580
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C
Rs. 540
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D
Rs. 570
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Solution

## The correct option is D Rs. 550Let x be fixed and y be the Variable expense average expense for 25 boarder =700Total expense =700×25=17500Average expense for 50 boarders =600Total expense=600×50=30000x+50y=30,000x+25y=17,500By solving25y=12,500=500x=30000−25000x=5000For 100 expense boardersTotal =5000+100×500=5000+50000=55000Average =55000100=550.

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