IPMAT Rohtak 2020 (QA) - 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? | PYQs + Solutions

IPMAT Rohtak 2020

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:

\newline

Number of managers = 459

Average spending =

\frac{x}{459}

After change:

\newline

Number of managers = 459 + 36 = 495

\newline

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:

\newline

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.