Sets Problem

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In country Z, 10% of the people do not have a university diploma but have the job of their choice, and 25% of the people who do not have the job of their choice have a university diploma. If 40% of the people have the job of their choice, what percent of the people have a university diploma?

Answer choices : 35% , 45% ,55% ,65%,75%

COrrect Answer : 45%

[liferocks]

Please use spoiler to post the ans

40% of the people have the job of their choice
hence (100-40) or 60% of the people does not have the job of their choice
25% of 60% i.e 15% of total people do not have the job of their choice have a university diploma
10% of the people do not have a university diploma but have the job of their choice
hence (40-10)% or 30% of the people have a university diploma and the job of their choice

[spoiler]so 15+30=45%[/spoiler] the people have a university diploma.

[Rahul@gurome]

100% - 40% = 60% of the people do not have the job of their choice.
25% of 60% = 15% people do not have the job of their choice but have University diploma.
This information can be represented in a venn diagram attached.

Yellow region represents people with University Diploma only.
Blue region reprsents people with their job of choice only.
In all 40% people have the job of their choice, but 10% out of them do not have a University diploma, which means 40% - 10% = 30% people have their job of choice as well the University Diploma.
So, Percent of people who have a University Diploma = 15% + 30% = 45%

The correct answer should be (B).