There were 35 students in a hostel. If the nu | vedclass

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Question

(B) Let the initial average expenditure per student be $Rs. x$.Then,the initial total expenditure $= 35x$.When $7$ more students join,the total number

Vedclass · Accepted Answer

$420$

Vedclass · Answer

(B) Let the initial average expenditure per student be $Rs. x$.Then,the initial total expenditure $= 35x$.When $7$ more students join,the total number of students becomes $35 + 7 = 42$.The new total expenditure becomes $35x + 42$.The new average expenditure per student is $\frac{35x + 42}{42}$.According to the problem,the new average is $x - 1$.So,$\frac{35x + 42}{42} = x - 1$.$35x + 42 = 42(x - 1)$.$35x + 42 = 42x - 42$.$42x - 35x = 42 + 42$.$7x = 84$.$x = 12$.The actual (initial) expenditure of the mess $= 35 	imes 12 = Rs. 420$.

There were $35$ students in a hostel. If the number of students increases by $7$,the expenses of the mess increase by $Rs. 42$ per day,while the average expenditure per head diminishes by $Rs. 1$. Find the actual expenditure of the mess (in $Rs.$).

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