There were 35 students in a hostel. If number of students increases by 7 , expenses of mess increase

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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 $Rs.$)

A

$480$

B

$420$

C

$520$

D

$460$

Solution

Suppose, the average expenditure was $Rs.\, x$

Then, total expenditure $=35 x$

When $7$ more students join the mess, total expenditure $=35 x+42$

Now, the average expenditure

$=\frac{35 x+42}{35+7}=\frac{35 x+42}{42}$

Now, we have $\frac{35 x+42}{42}=x-1$

$\therefore \quad x=12$

Thus, the actual expenditure of the mass $=35 \times 12=2420$

Standard 13

Quantitative Aptitude

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