There are 35 students in a hostel. If the num | vedclass

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(D) Let the original total expenditure be $Rs. x$.Original average expenditure per student $= \frac{x}{35}$.When the number of students increases by $

Vedclass · Accepted Answer

$420$

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(D) Let the original total expenditure be $Rs. x$.Original average expenditure per student $= \frac{x}{35}$.When the number of students increases by $7$,the new number of students $= 35 + 7 = 42$.The new total expenditure $= Rs. (x + 42)$.New average expenditure per student $= \frac{x + 42}{42}$.According to the problem,the average expenditure decreased by $Rs. 1$,so:$\frac{x}{35} - \frac{x + 42}{42} = 1$.Taking the least common multiple $(LCM)$ of $35$ and $42$,which is $210$:$\frac{6x - 5(x + 42)}{210} = 1$.$6x - 5x - 210 = 210$.$x = 210 + 210 = 420$.Therefore,the actual original expenditure of the mess is $Rs. 420$.

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

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