Question

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

• A. 280 days
• B. 260 days
• C. 290 days
• D. 252 days

Hint:

Reset at day 5: the food left feeds 120 men for 195 days. With only 90 men left, multiply 195 by 120/90.

Answer 1

The Correct Option is B

Step 1: Use inverse proportion instead of totals.
With a fixed stock of food, men and days are inversely proportional. More mouths means fewer days, and fewer mouths means more days.
\[ M_{1} \times D_{1} = M_{2} \times D_{2} \]

Step 2: Fix the starting point correctly.
The deaths happen on day 5, so reset the clock there.
On day 5, food remaining is enough for 120 men for $200 - 5 = 195$ days.
This is the key move: never compare against the original 200 days, because 5 days of food is already gone.

Step 3: Apply the inverse relation.
Here $M_{1} = 120$, $D_{1} = 195$, and $M_{2} = 90$.
\[ 120 \times 195 = 90 \times D_{2} \]
\[ 23400 = 90 D_{2} \]
\[ D_{2} = 260 \]

Step 4: See the same thing as a ratio.
The number of men falls from 120 to 90, a ratio of $3 : 4$ in favour of longer lasting food.
So the days must rise by $\dfrac{4}{3}$:
\[ 195 \times \frac{4}{3} = 65 \times 4 = 260 \]

Step 5: Rule out the rest.
280 days would need $\dfrac{280}{195} \approx 1.44$ times the stretch, which would mean roughly 83 men, not 90.
290 days would need about 81 men.
252 days would need about 93 men.
Only 260 matches exactly 90 men.

Final Answer:
The food lasts a further 260 days after the epidemic. \[ \boxed{260 \text{ days}} \]