Question:medium

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?

Updated On: Jul 15, 2026
  • 20
  • 45
  • 90
  • 180
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The Correct Option is C

Approach Solution - 1

Step 1: Understanding the Question.
The same quantity of food can serve either 450 students or 270 cops. After 300 students have already eaten, we need to find how many cops the remaining food can serve.

Step 2: Key Formula or Approach.
Since the food quantity is fixed, we can convert leftover student-meals into cop-meals using the ratio 270 cop-meals for every 450 student-meals.

Step 3: Detailed Explanation.
Total food = enough for 450 students.
After 300 students eat, the food left over is enough for:
\[ 450 - 300 = 150 \text{ students} \]
Convert this using the ratio 270 cop-meals for 450 student-meals:
\[ 150 \times \frac{270}{450} = 150 \times 0.6 = 90 \]

Step 4: Final Answer.
The remaining meal can feed 90 cops. \[ \boxed{90} \]
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Approach Solution -2

This can also be solved by setting up a direct proportion. The full food supply serves 450 students, which is the same as 270 cops, so the ratio 450 students : 270 cops describes the whole stock of food. After 300 students eat, the remaining food would have served \( 450 - 300 = 150 \) more students, so we can form the proportion \( 450 : 270 :: 150 : x \), where \( x \) is the number of cops the remaining food can feed. Cross-multiplying gives \( 450x = 270 \times 150 = 40500 \), so \( x = 90 \). Let's verify each option using this cross-multiplication.

  1. Option (A): 20: Cross-multiplying, \( 450 \times 20 = 9000 \), which does not equal \( 270 \times 150 = 40500 \), so this option breaks the proportion.
  2. Option (B): 45: Here \( 450 \times 45 = 20250 \), still far from \( 40500 \), so the proportion does not hold.
  3. Option (C): 90: Here \( 450 \times 90 = 40500 \), which exactly equals \( 270 \times 150 = 40500 \), so the proportion balances perfectly.
  4. Option (D): 180: Here \( 450 \times 180 = 81000 \), which is double \( 40500 \), so this option overshoots what the proportion allows.

Only \( x = 90 \) satisfies the cross-multiplied proportion \( 450 : 270 :: 150 : x \) built from the food supply's fixed capacity.

Therefore, the correct answer is 90.

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