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- Quantitative Aptitude
A professional institute's total expenditure on students for a particular course is partly fixed and partly varies linearly with the number of students. The average expense per student is $Rs.\,615$ when there are $24$ students and $Rs.\,465$ when there are $40$ students. What is the average expense when there are $60$ students ? (in $Rs.$)
$370$
$450$
$350$
$390$
Solution
Let the partly fixed expenditure be $x$.
And that partly varying be $y$
Then, $x+24 y=615 \times 24$ …$(1)$
Again, $x+40 y=465 \times 40$ ….$(2)$
Solving equations $(1)$ and $(2),$ we get
$x+24 y=615 \times 24$
$x+40 y=465 \times 40$
$-$ $-$ $-$
______________________
$16 y=18600-14760=3840$
$\Rightarrow \quad y=\frac{3840}{16}=240$
Putting the value of $y$ in equation $(1),$ we get $x=615$ $\times 24-24 \times 375$
$x=9000$
Now, when there are $60$ students
Average $=\frac{9000+240 \times 60}{60}$
$=\frac{9000+14400}{60}=\frac{23400}{60}=Rs.\, 390$
