There was one mess for 30 boarders in a certa | vedclass

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Question

(C) Let the initial average expenditure per boarder be $Rs.\, x$.Total initial expenditure for $30$ boarders $= 30x$.When the number of boarders incre

Vedclass · Accepted Answer

$360$

Vedclass · Answer

(C) Let the initial average expenditure per boarder be $Rs.\, x$.Total initial expenditure for $30$ boarders $= 30x$.When the number of boarders increases by $10$,the new number of boarders $= 30 + 10 = 40$.The new total expenditure $= 30x + 40$.The new average expenditure per head $= \frac{30x + 40}{40}$.According to the problem,the average expenditure per head decreases by $Rs.\, 2$,so:$\frac{30x + 40}{40} = x - 2$$30x + 40 = 40(x - 2)$$30x + 40 = 40x - 80$$10x = 120$$x = 12$.The actual monthly expenses $= 30 	imes x = 30 	imes 12 = Rs.\, 360$.

There was one mess for $30$ boarders in a certain hostel. On the number of boarders being increased by $10,$ the expenses of the mess were increased by $Rs.\, 40$ per month while the average expenditure per head diminished by $Rs.\, 2.$ Find out the actual monthly expenses (in $Rs.$).

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