What percent of a group of people are men who are left-handed?

If the number of people are P and the number of men who are left-handed is L, then the required percentage = \(\frac{L }{ P}\) * 100. We will need the values of L and P to answer the question.

From statement I alone, we know that 15 percent of the men are left-handed. Let there be M men. Then, 15% of M are left handed i.e. \(\frac{3M}{20}\) are left-handed men.
But, we do not know the total number of people since we do not know the number of women in the group. Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone, we know that 10 percent of the women are left-handed. Let there be W women. Then, 10% of W are left handed i.e. \(\frac{W}{10}\) are left-handed women.
But, we do not know the total number of people since we do not know the number of men in the group. Statement II alone is insufficient. Answer options B can be eliminated. Possible answer options are C or E.

Combining the statements I and II, we have the following:
From statement I, we have M men and \(\frac{3M}{20}\) are left-handed men. From statement II, we have W women and \(\frac{M}{10}\) are left-handed women.
We can also infer that there are a total of (M+W) people in the group.

Therefore, required percentage = \(\frac{3M}{20}\) + \(\frac{W}{10}\) / (M+W) *100 = \(\frac{(3M + 2W) }{ (20M + 20 W)}\) * 100.
We cannot evaluate this expression to find out the percentage until we have the values of M and W. The combination of statements is insufficient. Answer option C can be eliminated.

The correct answer option is E.

Hope that helps!