Question

A military camp has provision for 63 men at least for 25 days. How many men must be transferred to another camp so that the food lasts for 30 days?

Answer 1

Hint: First, we should know the concept of the fact that more men will eat more food . Then, let us assume the number of men is x for 30 days. Then, by using the two conditions as 25 days= food for 63 men and 30 days= food for x men, we get the number of men for 30 days as 53. Then, we need to get the number being transferred to another camp for the food to last 30 days is given by the subtraction of the men for 30 days from men for 25 days.

Complete step-by-step answer:
In this question, we are supposed to find the number of men transferred to another camp to get the food that lasts for 30 days.
So, we should know the concept of the fact that more men will eat more food.
Then, the condition given in the question states that:
25 days= food for 63 men
Now, we don’t know the number of men who can survive for 30 days.
So, let us assume the number of men be x.
Now, the same condition for the 30 days is given by:
30 days= food for x men
Then, by using the above two conditions and equating them as food is same in both the conditions.
So, the above expression looks as:
$30\times x=63\times 25$
So, by solving the above equation we get the number of men for 30 days which is x as:
$\begin{align}
  & x=\dfrac{63\times 25}{30} \\
 & \Rightarrow x=53 \\
\end{align}$
So, the above expression gives the number of men for 30 days as 53.
But, now we need to get the number being transferred to another camp for the food to last 30 days is given by the subtraction of the men for 30 days from men for 25 days.
So, the number of men transferred is given by:
$63-53=10$
So, 10 men are transferred to another camp for the food to last for 30 days.
Hence, the number of men being transferred is 10.

Note: For these kind of questions, we may occur only one kind of mistake is that we take the number of days directly proportional to the number of men which gives expression as:
$30\times 25=63\times x$ Now, by solving the above expression, we get the value of x as 12 which is an incorrect approach. So, we should be careful with the condition that the number of men will always be inversely proportional to the food required or more men will eat more food.