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

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(A) Let the original average expenditure per student be $x$ $Rs$.The original total expenditure for $35$ students is $35x$ $Rs$.When the number of stu

Vedclass · Accepted Answer

$420$

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(A) Let the original average expenditure per student be $x$ $Rs$.The original total expenditure for $35$ students is $35x$ $Rs$.When the number of students increases by $7$,the new number of students becomes $35 + 7 = 42$.The new total expenditure becomes $35x + 42$ $Rs$.The new average expenditure per student is $(35x + 42) / 42$.According to the problem,the new average expenditure is $(x - 1)$ $Rs$.So,$(35x + 42) / 42 = x - 1$.Multiplying both sides by $42$,we get $35x + 42 = 42(x - 1)$.$35x + 42 = 42x - 42$.$42x - 35x = 42 + 42$.$7x = 84$.$x = 12$ $Rs$.The original expenditure of the mess is $35 	imes x = 35 	imes 12 = 420$ $Rs$.

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 decreases by $Rs. 1$. Find the original expenditure of the mess in $Rs$.

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