Discussion
Work in a fort 300 men had provisions for 90 days after 20 days 50 men left the fort. How long would the food last at the same rate?
Answer: C
The food will last 84 days more.
After 20 days the provisions left are enough for 300 men for 70 more days. That stock is now shared by 300 - 50 = 250 men:
\[ \begin{aligned} 300 \times 70 &= 250 \times d \\ d &= \frac{21000}{250} = 84\ \text{days} \end{aligned} \]
80 days and 160 days come from forgetting that 20 days have already passed or from using the wrong number of men; with fewer men the food must last longer than 70 days, but only in the ratio 300 : 250.
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