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.
Ratio = 18 : 26 = 9 : 13
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