Question

A mess contractor can either serve 450 students with the meal that he prepares or can cater to 270 cops with the same meal. If 300 students have already eaten in the mess, how many cops can be fed with the remaining meal?

• A. 20
• B. 45
• C. 90
• D. 180

Answer 1

The Correct Option is C

The correct option is (C): 160.

Answer 2

The contractor's meal supply can feed 450 students or 270 cops, so the food quantity is a fixed amount expressed either way. After 300 students have eaten, we need how many cops the remaining food can feed. Let's check which option matches the remaining food supply.

1. Option (A): 20: Feeding 20 cops uses only a very small fraction of the total food, far less than the one third of the supply that remains after 300 of 450 students have eaten. This is too low.
2. Option (B): 45: 45 cops is exactly half of the 90 cops the remaining third of the food can support, so this option undercounts the leftover food by half.
3. Option (C): 90: The food for 450 students is the same fixed quantity as the food for 270 cops. After 300 students eat, food for 450 - 300 = 150 students remains, which is one third of the total. One third of 270 cops is 90, so the remaining food feeds exactly 90 cops.
4. Option (D): 180: 180 cops would need two thirds of the total food supply, but only one third of the food is left after 300 students have eaten, so this overstates the remaining food.

The remaining one third of the food supply, converted from student-meals to cop-meals, feeds exactly 90 cops.

Therefore, the correct answer is 90.

Answer 3

The contractor's food supply is a fixed quantity that can serve 450 students or 270 cops, so the rate of food consumption can be converted directly between the two units. Since 450 student-meals use the same food as 270 cop-meals, one student-meal is equivalent to \( \frac{270}{450} = \frac{3}{5} \) of a cop-meal. The 300 students who already ate therefore consumed food equal to \( 300 \times \frac{3}{5} = 180 \) cop-meal equivalents. Since the total capacity is 270 cop-meals, the remaining food can feed \( 270 - 180 = 90 \) cops. Let's check each option using this conversion.

1. Option (A): 20: If only 20 cop-meals remained, the food already consumed would equal \( 270 - 20 = 250 \) cop-meal equivalents, which converts back to \( 250 \times \frac{5}{3} \approx 416.7 \) student meals, far more than the 300 students who actually ate.
2. Option (B): 45: This would mean \( 270 - 45 = 225 \) cop-meal equivalents were already consumed, converting to \( 225 \times \frac{5}{3} = 375 \) student meals, still more than the 300 that were actually served.
3. Option (C): 90: This means \( 270 - 90 = 180 \) cop-meal equivalents were consumed, converting back to \( 180 \times \frac{5}{3} = 300 \) student meals, exactly matching the 300 students who already ate.
4. Option (D): 180: This would mean only \( 270 - 180 = 90 \) cop-meal equivalents were consumed, converting to \( 90 \times \frac{5}{3} = 150 \) student meals, well short of the 300 students actually served.

Converting the 300 already-served student meals directly into cop-meal equivalents shows exactly 180 cop-meals worth of food is used up, leaving 90 cop-meals of food remaining.

Therefore, the correct answer is 90.