Question

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?

Answer 1

Hint: Assume the food consumption of an individual person per day to be x.
Then find the total food requirement and total food availability.
After that find the food consumed by 120 people in five days and then find the remaining food and new food consumption rate.

Complete step-by-step answer:
Let us assume required food per person per day = $ x $
So, food required for 120 people for 1 day will be $ 120 \times x = 120x $
since, it given in question food is available for 200 days for 120 people
Therefore, total available food = $ 120x \times 200 $
 $ \Rightarrow $ Total available food = $ 24000x $
Now, since there were 120 men alive in first 5 days so food consumed in 5 days will be:
 $ = {\text{food required for each person per day}} \times {\text{no}}{\text{. of days}} \times {\text{no}}{\text{.of person}} $
 $ \begin{gathered}
   = x \times 5 \times 120 \\
   = 600x \\
\end{gathered} $
Food left after 5 days = Total available food – Total consumed food
                                    $ \begin{gathered}
   = 24000x - 600x \\
   = 23400x \\
\end{gathered} $
As 30 people died after 5 days, remaining people are 120 – 30 = 90
Food required for 90 people for 1 day = $ 90x $
No of days food can be consumed for 90 people:
 $ = \dfrac{{{\text{food left}}}}{{{\text{food consumption per day}}}} $
 $ \begin{gathered}
   = \dfrac{{23400x}}{{90x}} \\
   = 260{\text{ days}} \\
\end{gathered} $
So, the remaining food will last for another 260 days

Note: This question can also be solved simply as:
 $ \begin{gathered}
  {\text{initial no}}{\text{. of men }} \times {\text{ no}}{\text{. of remaining days = remaining no}}{\text{. of men }} \times {\text{ new no}}{\text{. of remaining days}} \\
   \Rightarrow 120 \times \left( {200 - 5} \right) = \left( {120 - 30} \right) \times D \\
   \Rightarrow 120 \times 195 = 90 \times D \\
   \Rightarrow D = \dfrac{{120 \times 195}}{{90}} = 260{\text{ days}} \\
\end{gathered} $