Question

In a fort, there was sufficient food for 200 soldiers for 31 days. After 27 days 120 soldiers left the fort. For how many extra days will the rest of the food last for the remaining soldiers?

Answer 1

Hint: We approach this question in such a way that we know at the start 200 soldiers had food for 31 days. After the passage of 27 days, 200 men still had food for 4 days but since 120 soldiers left the fort so we can say that only 80 soldiers are left in the fort. We will suppose the food be last for $x$ days for the 80 soldiers and then we will just use the indirect proportion technique because we know that fewer soldiers, more days for the food to last, and on simplifying the ratios we get the required number of days for which the food will last for 80 soldiers after 27 days.

Complete step by step answer:
It is given that 200 soldiers had food for 31 days.
After 27 days, 200 soldiers still had food for 4 days.
Since 120 soldiers left the fort so $200 - 120 = 80$ soldiers are left in the fort.
Now, let us suppose that 80 soldiers had food for $x$ number of days.
We know that we have the case of indirect proportion here because as the number of soldiers will decrease food will last for a greater number of days.
$ \Rightarrow 80:200::4:x$
Convert the expression in fraction form,
$ \Rightarrow \dfrac{{80}}{{200}} = \dfrac{4}{x}$
Cross multiply the terms,
$ \Rightarrow 80x = 200 \times 4$
Divide both sides by 80,
$ \Rightarrow x = \dfrac{{200 \times 4}}{{80}}$
Simplify the terms,
$ \Rightarrow x = 10$
As the food was already for 4 days. Then,
$ \Rightarrow $ Extra days $ = 10 - 4$
Subtract the values,
$ \Rightarrow $ Extra days $ = 6$

Hence, we can say that the 80 soldiers had food for the 6 extra days.

Note: For such types of questions, just keep in mind the concept of inverse proportion that when one value decreases then the other value increases at the same rate. Likewise, as the number of men will decrease, food will last for a greater number of days. Also, do the comparisons very carefully in such types of questions.