Question

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

Answer 1

Correct option is A. 300
It is given that after $$4$$ days, out of $$28$$ days, the fort had enough food for $$1200$$ soldiers for $$(28-4=24)$$ days.

Let $$x$$ be the number of soldiers who left the fort.

Number of soldiers	$$1200$$	$$1200-x$$
Number of days for which food lasts	$$24$$	$$32$$

Since, the number of soldiers and the number of days for which the food lasts are in inverse variation, we have :

$$\Rightarrow$$ $$1200\times 24=(1200-x)\times 32$$

$$\Rightarrow$$ $$\dfrac{1200\times 24}{32}=1200-x$$

$$\Rightarrow$$ $$900=1200-x$$

$$\Rightarrow$$ $$x=1200-900$$

$$\Rightarrow$$ $$x=300$$

$$\therefore$$ The soldiers which left the fort are $$300$$.