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      Question

      In a job fair, 50% of the people are graduates, one

      fifth of them are post graduates and rest are double graduates. If three-fourth of the graduates, 60% of the post graduates and half of the double graduates are unemployed, what percentage of total people is already employed?
      A 35.5% Correct Answer Incorrect Answer
      B 40.5% Correct Answer Incorrect Answer
      C 38% Correct Answer Incorrect Answer
      D 42% Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let the total number of people be x [if gte msEquation 12]>x [if !msEquation]-->[endif]--> [if gte msEquation 12]>∴ [if !msEquation]-->[endif]--> According to the question, Number of graduates = `(1)/(2)` x Number of post graduates = `(1)/(5)` [if gte msEquation 12]> 1 5 x [if !msEquation]-->[endif]--> x Number of double graduates = x [if gte msEquation 12]>x [if !msEquation]-->[endif]--> - `(1)/(2)` x [if gte msEquation 12]> 1 2 x [if !msEquation]-->[endif]--> - `(1)/(5)` [if gte msEquation 12]> 1 5 x [if !msEquation]-->[endif]--> x= `(3)/(10)` x [if gte msEquation 12]> 3 10 x [if !msEquation]-->[endif]--> Number of graduates who are unemployed = `(3)/(4)` [if gte msEquation 12]> 3 4 [if !msEquation]-->[endif]--> × `(1)/(2)` [if gte msEquation 12]> 1 2 x [if !msEquation]-->[endif]--> x= `(3x)/(8)` Number of post graduates who are unemployed = `(3)/(5)` [if gte msEquation 12]> 3 5 [if !msEquation]-->[endif]--> × `(1)/(5)` [if gte msEquation 12]> 1 5 x [if !msEquation]-->[endif]--> x = `(3x)/(25)` [if gte msEquation 12]> 3x 25 [if !msEquation]-->[endif]--> Number of double graduates who are unemployed = `(1)/(2)` [if gte msEquation 12]> 1 2 [if !msEquation]-->[endif]--> × `(3)/(10)` x = `(3x)/(20)` [if gte msEquation 12]> 3x 20 [if !msEquation]-->[endif]--> [if gte msEquation 12]>∴ [if !msEquation]-->[endif]--> Total number of people who are employed = x [if gte msEquation 12]>x [if !msEquation]-->[endif]--> - `(3x)/(8)` [if gte msEquation 12]> 3x 8 [if !msEquation]-->[endif]--> - `(3x)/(25)` [if gte msEquation 12]> 3x 25 [if !msEquation]-->[endif]--> - `(3x)/(20)` [if gte msEquation 12]> 3x 20 [if !msEquation]-->[endif]--> = `(200x - 75x - 24x - 30x)/(200)` = [if gte msEquation 12]> 71x 200 [if !msEquation]-->[endif]--> `(71x)/(200)` The percentage of people who are employed = `(71x)/(200)` X 100 = 35.5%

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