A professional institute's total expenditure | vedclass

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(D) Let the fixed expenditure be $x$ and the variable expenditure per student be $y$.Total expenditure for $n$ students is given by $E = x + ny$.The a

Vedclass · Accepted Answer

$390$

Vedclass · Answer

(D) Let the fixed expenditure be $x$ and the variable expenditure per student be $y$.Total expenditure for $n$ students is given by $E = x + ny$.The average expense per student is $A = \frac{E}{n} = \frac{x}{n} + y$.For $24$ students,$A = 615$,so $\frac{x}{24} + y = 615 \Rightarrow x + 24y = 14760$ ...$(1)$For $40$ students,$A = 465$,so $\frac{x}{40} + y = 465 \Rightarrow x + 40y = 18600$ ...$(2)$Subtracting equation $(1)$ from $(2)$:$(x + 40y) - (x + 24y) = 18600 - 14760$$16y = 3840 \Rightarrow y = 240$.Substituting $y = 240$ into equation $(1)$:$x + 24(240) = 14760$$x + 5760 = 14760 \Rightarrow x = 9000$.For $60$ students,the average expense is:$A = \frac{x}{60} + y = \frac{9000}{60} + 240 = 150 + 240 = 390$.Thus,the average expense is $Rs.\,390$.

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