Discussion
A garrison of 500 men had provision for 27 days. After 3 days a reinforcement of 300 men arrived. For how many more days will the remaining food last now?
Answer: A
Work in man-days, the quantity that stays fixed however the numbers change. After 3 days the provision left is what 500 men would eat in the remaining \( 27 - 3 = 24 \) days:
\[ \text{food remaining} = 500 \times 24 = 12{,}000 \text{ man-days} \]
The reinforcement brings the strength to \( 500 + 300 = 800 \), so
\[ \text{days} = \frac{12{,}000}{800} = 15 \]
Note the two traps: the 27 must be reduced to 24 before anything else, and the 300 is an addition to the garrison rather than the new total.
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