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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?
Solution
\[\text{ It is given that after 4 days, out of 28 days, the fort had enough food for 1200 soldiers for (28 - 4 = 24) days } . \]
\[\text{ Let x be the number of soldiers who left the fort } . \]
| Number of soldiers | 1200 | 1200-x |
| Number of days for which food lasts | 24 | 32 |
\[\text{ Since the number of soldiers and the number of days for which the food lasts are in inverse variation, we have: } \]
\[1200 \times 24 = \left( 1200 - x \right) \times 32\]
\[ \Rightarrow \frac{1200 \times 24}{32} = 1200 - x\]
\[ \Rightarrow 900 = 1200 - x\]
\[ \Rightarrow x = 1200 - 900\]
\[ = 300\]
\[\text{ Thus, 300 soldiers left the fort } .\]
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