Expert: Scott A Wilson - 11/4/2009

Question
A garrison of 2000 men has provisions for 54days. At the end of 15days a reinforcement arrives and it is found that now the provisions would last for 20days more. What is the strength of reinforcement?

Answer
Since there are 2,000 men and there are 54 days of food, that means that there is enough food for 54*2000 = 108,000 days.

Now we fed these 2,000 men for 15 days, so the amount of food used is 2,000*15=30,000 days worth.
If we take 108,000 - 30,000, the answer is 78,000.

Now since we only have enough food for 20 more days, that means there are 78,000/20 men.
78,000/20 = 7,800/2 = 3,900.  This means we have 3,900 men at this point, and since we originally had 2,000 men, we've have gotten 1,900 more men in the reinforcemet.