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?

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%