There are $459$ students in a hostel. If the number of students is increased by $36,$ the expenses of the mess are increased by $R s . 81$ Per day while the average expenditure per head is reduced by $R s . 1.$ Find the original expenditure of the mess?

7344

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7314

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7324

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7334

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Solution

The correct option is B: $R s . 7344$
Let the average expenditure per head be $R s . x$
Number of students $= 495$
Total expenditure $= 459 x$
$36$ students joined then total expenditure $= 459 x + 81$
Average expenditure after $36$ students increased $= \frac{459 x + 81}{495}$
And, it is given that the average expenditure reduced by $R s . 1$ after student increment.
$∴ \frac{459 x + 81}{495} = x - 1$
$\Rightarrow 459 x + 81 = 495 x - 495$
$\Rightarrow 81 + 495 = 495 x - 459 x$
$\Rightarrow 81 + 495 = 36 x$
$\Rightarrow x = \frac{576}{36}$
$∴ x = 16$
So, Original expenditure of the mess $= 16 \times 459 = R s . 7344$

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There are 459 students in a hostel. If the number of students is increased by 36, the expenses of the mess are increased by Rs. 81 Per day while the average expenditure per head is reduced by Rs. 1. Find the original expenditure of the mess?

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