120 men had a food provision for 200 days. After 5 days, 30 men died due to an epidemic. How long would their remaining food last ?

# 120 men had a food provision for 200 days. After 5 days, 30 men died due to an epidemic. How long would their remaining food last ?

1. A
120
2. B
140
3. C
260
4. D
220

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### Solution:

Concept: We will find the total food requirement and total food availability, and let the required food consumption of an individual person per day be $x$, then  after finding the food consumed by 120 people in 5 days, we will find the remaining food and the new food consumption rate.
Let the required food per person per day $=x$
Therefore, required food for 120 people for 1 day $=120×x$
$=120x$
Given that, food is available for 200 days for 120 people.
$⇒$Total available food $=120x×200$
$⇒$Total available food $=24000x$
Since, there were 120 men alive in first 5 days so that food consumed in 5 days
= food required for each person per day$×\mathit{number of days}×\mathit{number of person}$
$⇒$120 men alive in first 5 days so that food consumed in 5 days $=x×5×120$
$⇒$120 men alive in first 5 days so that food consumed in 5 days$=600x$
Food left over after five days equals total food available minus total food consumed.
$=24000x-600x$
$=23400x$
As, 30 people died after 5 days, remaining people $=120-30=90$
Food required for 90 people for 1 day $=90x$
Number of days food can be consumed for 90 people $=\frac{\mathit{food left}}{\mathit{food consumption per day}}$
$=\frac{23400x}{90x}$

Remaining food will last for another 260 days.
Hence, the correct answer is option (3).
Syllabus: CBSE

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