Question

120 men had provisions for 200 days. After 5 days, 30 men died due to an epidemic. The remaining food will last for how many days.

Answer 1

Hint: According to the given question, provisions are available for 120 men for 200 days is given and here we firstly calculate the total provision consumed by 1 man. Also, we will find total provision consumed in 5 days as it is given after 5 days 30 men died. So, we will calculate how my provision and men’s left. At last, we will calculate the number of days the food will remain.

Complete step-by-step answer:
It is clearly given in the question, that provisions are available for 120 men for 200 days that is \[120men \to 200days\] .
Here, we will calculate the total provision consumed by 1 man in 120 days is number of men’s \[ \times \] number of days
By substituting given values we get,
\[ \Rightarrow 120 \times 200\]
On multiplying we get,
Therefore, the total provision consumed by 1 man \[ = 24000\] days
As, we know after 5 days 30 men died. So, the total provision consumed in 5 days is \[120 \times 5\] which is equal to 600 days.
Hence, the total provisions left \[ = \] the total provision consumed by 1 man in 120 days \[ - \] the total provision consumed in 5 days.
By putting the calculated values we get,
\[ \Rightarrow 24000 - 600\]
On subtracting we get,
So, the total provisions left \[ = 23400\] days
Now, we will calculate number of men’s left that is \[120 - 30\] which is equal to 90 men (As 30 person died)
At last, we will find out the number of days for which the food remain \[ = \dfrac{{Total\,{\rm{ }}provision\,{\rm{ }}left}}{{Number\,{\rm{ }}\,of{\rm{ }}\,men's{\rm{ }}\,left}}\]
After substituting the values we get,
\[ \Rightarrow \dfrac{{23400}}{{90}}\]
On dividing we get,
\[ \Rightarrow 260\]
Hence, the remaining food will last for 260 days.

Note: To solve these types of questions, firstly read the statement step by step and convert them in the form of equations. We can also assume the food consumed for each man is x and just multiply the total number of men with x for better understanding of the concept used as shown above.