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. $550$
• B. Rs. $580$
• C. Rs. $540$
• D. Rs. $570$

Answer 1

Answer: (A)

Rs. $550$

Let x be fixed and y be the Variable expense average expense for $25$ boarder $=700$
Total expense $=700\times 25=17500$
Average expense for $50$ boarders $=600$
Total expense$=600\times 50=30000$
$x+50y=30,000$
$x+25y=17,500$
By solving
$25y=12,500=500$
$x=30000-25000$
$x=5000$
For $100$ expense boarders
Total $=5000+100\times 500=5000+50000=55000$
Average $=\frac{55000}{100}=550$.