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A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is :

  • A.12
  • B.36
  • C.42
  • D.54

Answer: C

Count the food in man-days, which does not change when men leave. After 10 days there remain \( 45 - 10 = 35 \) days of provision for 150 men:

\[ \text{food remaining} = 150 \times 35 = 5{,}250 \text{ man-days} \]

With 25 men gone the strength is \( 150 - 25 = 125 \), so

\[ \text{days} = \frac{5{,}250}{125} = 42 \]

Fewer men must make the food last longer, so any answer below 35 is wrong on inspection - which disposes of 12 at once.

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