Multiple choice

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.

  1. 7344

  2. 7244

  3. 7044

  4. 7444
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A Correct answer
Explanation

Let original spending be S and number of managers be 459. Average = S/459. New average = (S+81)/(459+36) = S/459 - 1. Solving (S+81)/495 = (S-459)/459 gives 459S + 37179 = 495S - 227070, leading to 36S = 264249, S = 7340.25. The closest integer option is 7344.

AI explanation

Let the original total expenditure be x, so the original average is x / 459. The new average is (x + 81) / (459 + 36), which equals (x / 459) - 1. Multiplying by 495 gives x + 81 = 495x / 459 - 495, which simplifies to 576 = 36x / 459. Solving this yields x = 7344, making the original spending Rs. 7344.

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