Arithmetic

Averages

Hard

Imagine that there are four hundred and fifty nine managers in a hotel. If the number of managers is enlarged by 36, the expenses of the food increased by Rs. eighty one per day while the average spending per head decreased by one. Find the original spending of the hotel on food?

7344

7244

7044

7444

✅ Correct Option: 1

Let original spending be x

Initial condition:

Number of managers = 459

Average spending = $\frac{x}{459}$

After change:

Number of managers = 459 + 36 = 495

Total spending = x + 81

New average = $\frac{x + 81}{495}$

Given: New average = Original average - 1

$\frac{x + 81}{495} = \frac{x}{459} - 1$

Cross multiply:

$459(x + 81) = 495x - (495 × 459)$

$459x + 37179 = 495x - 227205$

$37179 + 227205 = 495x - 459x$

$264384 = 36x$

$x = 7344$

Therefore, the original spending was Rs. 7344 per day.

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