A group of people can finish 30% of a piece of work in 60 days. If there were 8 more people, 75% of the work could be done in 50 days. What was the initial number of people?

Let the initial number of people be M and the work done by one person in one day be k. Since 30 percent of the work takes 60 days, the equation is M times k times 60 equals 0.30, meaning the total work is 200 times M times k. The second condition states that 75 percent of the work takes 50 days with 8 more people, so (M plus 8) times k times 50 equals 0.75. Substituting the total work from the first equation into the second gives (M plus 8) times k times 50 equals 0.75 times 200 times M times k. Solving this equation yields 50M plus 400 equals 150M, resulting in M equals 4, which falls under the none of these category.

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