100 + 50 = 150 people for second ratio
100 : 15 = 150 : n
15 (150) = 2250
2250 ÷ 100 = 22.5 days or 22 days and 12 hrs.
To check, the product of the means and extremes must be equal.
100 (22.5) = 15 (150)
2250 = 2250
Therefore, the answer to your question is 22.5 days.
