In a college, 150 students of MBA are enrolled. The ratio of boys and girls is 7 : 8 respectively. There are three disciplines namely marketing , HR and finance in the college. In marketing discipline there are 50% girls of their total number and the boys are 40% of their total number. In HR discipline, girls are 30% of their total number. Finance discipline has girls, 20% of their total number and boys 30% of their total number. 7 boys and 9 girls are in HR and marketing both. 6 boys and 7 girls are in HR and finance both. 5 boys and 8 girls are in marketing and finance both. 2 boys and 3 girls are enrolled in all three disciplines.
Total Number of students = 150
Ratio of Boys to Girls = 7 : 8
Total Number of Girls = $$\frac{8}{15}$$ x 150 = 80
Total number of Boys = $$\frac{7}{15}$$ x 150 = 70
Number of girls in Marketing = $$\frac{50}{100}$$ x 80 = 40
Number of boys in marketing = $$\frac{40}{100}$$ x 70 = 28
Number of girls in HR = $$\frac{30}{100}$$ x 80 = 24
Number of girls in Finance = $$\frac{20}{100}$$ x 80 = 16
Number of boys in Finance = $$\frac{30}{100}$$ x 70 = 21
Number of boys in HR = 70 - 28 - 21 = 21
Number of boys only in Marketing = 28 - (7 + 5 - 2) = 18
Number of girls only in Marketing = 40 - (9 + 8 - 3) = 26
Number of boys only in HR = 21 - (7 + 6 - 2) = 10
Number of girls only in HR = 24 - (9 + 7 - 3) = 11
Number of boys only in Finance = 21 - (6 + 5 -2) = 12
Number of girls in Finance = 16 - (7 + 8 - 3) = 4
The diagram below shows the number of number of students(both boys and girls together) in each discipline, both the disciplines and all the disciplines.
Percentage of students in all three disciplines = $$\frac{5}{150}$$ x 100 = 3.3%
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