Question

1200 soldiers in a fort had enough food for 28 days. After 4 days, some soldiers were sent to another fort and thus the food lasted for 32 more days. How many soldiers left the fort?

Answer 1

Hint – In this question assume the number of soldiers which left after 4 days to be a variable. As they were sent to another fort after 4 days so they must have eaten for 4 days thus the ration left will be of (28-4) days and after some of soldiers were sent to other fort ,the food lasted for 32 days So as we see that when the number of soldiers decreases, the food would last for more days thus there is an inverse variation between soldiers and number of days.Formulate an equation involving variables and get the answer.

Complete step-by-step answer:
Let the number of soldiers sent to another fort after 4 days be x soldiers.
Now 1200 soldiers had enough food for 28 days.
The number of soldiers who were sent to another fort lasted for 4 days in this fort.
So the number of days left for enough food = (28 – 4) = 24 days.
So 1200 soldiers had enough food for 24 days after the 4 days.
Therefore 1200 soldiers = 24 days.
Now when (x) soldiers sent to another fort after 4 days the food left for another 32 days
Therefore (1200 – x) soldiers = 32 days.
So as we see that when the number of soldiers decreases, the food would last for more days thus there is an inverse variation between soldiers and number of days.
Therefore we get,
$ \Rightarrow 1200 \times 24 = \left( {1200 - x} \right)32$
 Now simplify the above equation we get,
$ \Rightarrow 1200 \times 24 = 1200 \times 32 - 32x$
$ \Rightarrow 32x = 1200\left( {32 - 24} \right) = 1200\left( 8 \right)$
$ \Rightarrow x = \dfrac{{1200 \times 8}}{{32}} = \dfrac{{1200}}{4} = 300$.
Therefore 300 soldiers left the fort after 4 days.
So this is the required answer.

Note – During the formulation of the equation make sure that we equate equal entities on both the sides. As In this case total soldiers multiplied with the total days of food are equalized only then the equation formed is valid, for example while calculating cost questions the prices are equated with each other. This concept is useful while solving general mathematics questions of this kind.