Question

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

Answer 1

Hint: For this we first let the number of soldiers left after transfer of some soldiers. Then calculating the first amount of food left after four days to the amount of food that last long for $ 32\,days $ to get the number of soldiers left in the fort.

Complete step-by-step answer:
Number of soldiers in fort before transfer = $ 1200 $
Food enough for = $ 28\;days $
Therefore, total food can be calculated by multiplying the number of soldiers with the number of days for which food is enough.
Total food = $ 28 \times 1200 $
Total food = $ 33600 $
Food consumed by $ 1200 $ soldiers in $ 4\,days $ = $ 4 \times 1200 $
Therefore, food consume by $ 1200 $ soldiers in $ 4\,days $ = 4800
Food left after $ 4\,days $ with them = total food – food consumed by $ 1200 $ soldiers in $ 4\,days $ .
 $ \Rightarrow $ Food left = $ 33600 - 4800 $
 $ \Rightarrow $ Food left = $ 28800 $ ………….(i)
This left food according to the question last long for $ 32\,\,days $ .
The number of soldiers left in the fort after transfer is n.
Then food required for n soldiers for $ 32\,days $ will be given as a product of number of soldiers and number of days food last long.
 $ \Rightarrow $ Total food = $ 32 \times n $
 $ \Rightarrow $ Total food = $ 32n $ ……………..(ii)
But from (i) we have food left and from (ii) we have total food required.
Therefore, we have
 $
  32n = 28800 \\
   \Rightarrow n = \dfrac{{28800}}{{32}} \\
   \Rightarrow n = 900 \;
  $
Hence, from above we see that there were $ 900 $ soldiers in the fort for which food lasted long for $ 32\,days. $
Which implies that $ 300 $ soldiers transferred from fort to another fort as earlier there were $ 1200 $ soldiers in fort
So, the correct answer is “ $ 300 $ ”.

Note: We can also find solutions to given problems in the ratio method. In this method we first let the number of soldiers left after transfer and then find the ratio of number soldiers to the ratio of total food to get value of number solider or required solution of the given problem.