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?

Show Hint

In “same meal for two groups” problems, convert everything to one unit (e.g., student-meals), then use ratios to switch groups.
Updated On: Jul 15, 2026
  • 20
  • 45
  • 90
  • 180
Show Solution

The Correct Option is C

Approach Solution - 1

Step 1: Let the total prepared food equal 1 whole unit. One student's portion is \( \frac{1}{450} \) of the total, and one cop's portion is \( \frac{1}{270} \) of the total.

Step 2: Feeding 300 students uses \( 300 \times \frac{1}{450}=\frac{2}{3} \) of the food, leaving \( 1-\frac{2}{3}=\frac{1}{3} \).

Step 3: The number of cops that can be fed with \( \frac{1}{3} \) of the food is \( \frac{1}{3} \div \frac{1}{270}=\frac{270}{3}=90 \).
\[ \boxed{90 \text{ cops}} \]
Was this answer helpful?
0
Show Solution

Approach Solution -2

Since the full stock of food serves either 450 students or 270 cops, these two figures are directly proportional to each other: 450 student-meals of food is worth the same as 270 cop-meals. The food remaining after 300 students have eaten is worth \( 450-300=150 \) student-meals. We can set up the proportion \( 450:270=150:x \) and check each option as a candidate value of \( x \).

  1. 20: Cross-multiplying, \( 450 \times 20=9000 \), which should equal \( 270 \times 150=40500 \); these do not match.
  2. 45: Cross-multiplying, \( 450 \times 45=20250 \), which does not equal 40500.
  3. 90: Cross-multiplying, \( 450 \times 90=40500 \), matching \( 270 \times 150=40500 \) exactly.
  4. 180: Cross-multiplying, \( 450 \times 180=81000 \), which does not equal 40500.

The proportion \( 450:270=150:x \) balances only when \( x=90 \), so 90 cops can be fed with the remaining food.

Therefore, the correct answer is 90.

Was this answer helpful?
0

Top Questions on Ratio and Proportion


Questions Asked in CLAT exam