Final answer:
Using the principle of inclusion-exclusion, it was determined that the percentage of youths who like to do something in their village only is 35%, which is not among the provided options. This suggests there might be an error in the question or answer choices.
Step-by-step explanation:
To solve the problem, we will use the principle of inclusion-exclusion. The principle allows us to find the proportion of youths who like one activity but not the other by taking into account the total percentage who like each activity and the percentage who like neither.
First, let's sum up the percentages of youths who like to do something in their village and those who like to go to foreign employment:
- 85% like to do something in their village.
- 60% like to go to foreign employment.
- 5% do not like either.
According to the principle of inclusion-exclusion, to find the percentage of youths who like to do something in their village only (and not go to foreign employment), we calculate:
Total liking village only = Percentage liking village - Percentage liking both
However, we do not have the percentage liking both directly. To find it, we must consider that:
Percentage liking both = (Percentage liking village + Percentage liking foreign employment) - (Total percentage) + Percentage liking neither
Plugging in the values:
Percentage liking both = (85% + 60%) - 100% + 5%
Percentage liking both = 145% - 100% + 5%
Percentage liking both = 50%
Now, to find the percentage who like to do something in their village only:
Total liking village only = 85% - 50%
Total liking village only = 35%
Therefore, the correct answer is neither of the options provided, suggesting there may be a typo in the question or the answer choices.