Question:

120 men had food provision for 200 days. After 5 days, 30 men died of an epidemic. The food will last for further

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Reset at day 5: the food left feeds 120 men for 195 days. With only 90 men left, multiply 195 by 120/90.
Updated On: Jul 17, 2026
  • 280 days
  • 260 days
  • 290 days
  • 252 days
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The Correct Option is B

Solution and Explanation

Step 1: Think in man days.
One man day is the food one man eats in one day. Total food stays fixed no matter how many men eat it, so counting man days is the safe way to handle this.
Total food \( = 120 \text{ men} \times 200 \text{ days} = 24000 \) man days.

Step 2: Subtract what the first 5 days consumed.
For those 5 days all 120 men were alive and eating.
Food used \( = 120 \times 5 = 600 \) man days.
Food left \( = 24000 - 600 = 23400 \) man days.

Step 3: Count the men who remain.
30 men died, so \( 120 - 30 = 90 \) men are left to share the remaining food.

Step 4: Divide the leftover food among the survivors.
\[ \text{Days} = \frac{23400}{90} = 260 \]

Step 5: A quick reasonableness check.
At full strength the food would have lasted 195 more days after day 5. Fewer men eat less, so the food must stretch beyond 195 days. It stretches by the factor \( \frac{120}{90} = \frac{4}{3} \), giving \( 195 \times \frac{4}{3} = 260 \). Same answer by a different route.

Step 6: Why the other options are wrong.
280 comes from ignoring the 5 days already eaten and doing \( 200 \times \frac{120}{90} \), which is \( 266.67 \), or from some other mismatch. Either way it overcounts the food.
290 is what you get by taking \( 260 + 30 \) or similar loose arithmetic, and it does not follow from the data.
252 does not come out of any correct step.
One more trap: the question asks for the food lasting further, meaning from day 5 onwards, not the total from day zero. The total would be \( 5 + 260 = 265 \) days, which is not an option, so 260 is clearly what is wanted.

Final Answer:
The remaining food will last 260 more days. \[ \boxed{260 \text{ days}} \]
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