Question

Military camp has provisions for \[300\] people consuming \[600\] grams daily for \[75\] days. They are joined by \[60\] more men and the daily ration was reduced by \[100\] grams. How long will the provisions last approximately?

Answer 1

Hint: The given problem is an inverse variation type that is, if an increase in one quantity increases results in the decrease in other quantity and vice versa then the quantities are inversely proportional. Here the increase in the number of persons decreases the provision thus, it is an inverse variation type.

Complete step by step answer:
It is given that the camp has provisions for \[300\] people for \[75\] days with \[600\] grams per day.
Then \[60\] more people joined which led to a decrease in the provision. We aim to find how many days the provisions will last after the increase in the number of people.
We know that if there is an increase or decrease in one quantity that leads to a decrease or increase in another quantity then the quantities are inversely proportional to each other.
Let us create a table using the given data

No. of persons	Grams per day	No. of days
\[300\]	\[600\]	\[75\]
\[300 + 60 = 360\]	\[600 - 100 = 500\]	x

Now we need to find the unknown value of x.
 \[300 \times 600 \times 75 = 360 \times 500 \times x\]
Let us re-arrange this for easy simplification.
 \[x = \dfrac{{300 \times 600 \times 75}}{{360 \times 500}}\]
Now let us cancel all the possible terms.
 \[x = \dfrac{{300 \times 6 \times 75}}{{360 \times 5}}\]
Let us simplify it further.
 \[x = \dfrac{{300 \times 6 \times 15}}{{360}}\]
Simplifying it further we get
 \[x = 5 \times 15\]
Thus, we get \[x = 75\]
That is, the provisions will last for \[75\] days.

Note: Unitary method can be divided in two methods, direct or indirect(inverse) variation. Since in the given problem, an increase in the number of persons decreases the provision thus, we have solved this problem by inverse variation method. We are also able to solve by finding the mean to this problem which is the average by using that we will be able to proceed to find the x.