In the grand city of Khem, the Royal Granary was precisely stocked to provide for its 10,000 inhabitants for 60 days. However, after 10 days of normal consumption, a delegation of 2,000 foreign merchants arrived, seeking refuge and food due to a regional crisis. The benevolent Pharaoh decreed they be fed from the same granary. Assuming all individuals consume food at the same steady rate, for how many *total* days from the initial stocking will the granary's food supply now last?
Correct: 51.67 days
First, calculate the total 'person-days' of food initially available:
Total Food = 10,000 inhabitants * 60 days = 600,000 person-days.
After 10 days, food consumed:
Consumed Food = 10,000 inhabitants * 10 days = 100,000 person-days.
Remaining food in the granary:
Remaining Food = 600,000 - 100,000 = 500,000 person-days.
Now, the population increases:
New Population = 10,000 (original) + 2,000 (merchants) = 12,000 individuals.
Calculate how many *additional* days the remaining food will last for the *new* population:
Days Remaining = Remaining Food / New Population = 500,000 person-days / 12,000 individuals = 500/12 = 125/3 days.
125/3 days is approximately 41.67 days.
The question asks for the *total* number of days from the initial stocking. We already passed 10 days, and the remaining food will last for another 41.67 days.
Total Duration = 10 days (initial) + 41.67 days (remaining) = 51.67 days.