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Home » Quantitative Aptitude » Arithmetic » Set Theory » all » DI Set Theory No 2

Directions: Read the following information carefully to answer the questions given below:

In a college, 150 students of MBA are enrolled. The ratio of boys to girls is 7 : 8. 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 while boys are 30% of their total number. Finance discipline has girls 20% of their total number and the boys are 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.
Important for :
IBPSPO
1
What percentage of students are enrolled in all three disciplines?
» Explain it
A
Boys =  7  × 150 = 70;  Girls =  8  × 150 = 80
15 15

Disciplines Boy Girl
Marketing, n(M) 28 40
HR, n(M) 21 24
Finance, n(F) 21 16
HR + Marketing, n (H ∩ M) 7 9
HR + Finance, n(H ∩ F) 6 7
Marketing + Finance, n (M ∩ F) 5 8
Marketing + Finance + HR, n (M ∩ F ∩ H) 2 3



Reqd% =  5  × 100 = 3.33%
150
2
What is the ratio of boys to girls only in Marketing discipline?
» Explain it
B
Boys =  7  × 150 = 70;  Girls =  8  × 150 = 80
15 15

Disciplines  Boy   Girl 
Marketing, n(M) 28 40
HR, n(M) 21 24
Finance, n(F) 21 16
HR + Marketing, n (H ∩ M) 7 9
HR + Finance, n(H ∩ F) 6 7
Marketing + Finance, n (M ∩ F) 5 8
Marketing + Finance + HR, n (M ∩ F ∩ H) 2 3


Reqd ratio = 18 : 26 = 9 : 13
3
The ratio of the number of boys in Marketing and Finance both to that of girls only in Finance is
» Explain it
C
Boys =  7  × 150 = 70;  Girls =  8  × 150 = 80
15 15

Disciplines  Boy   Girl 
Marketing, n(M) 28 40
HR, n(M) 21 24
Finance, n(F) 21 16
HR + Marketing, n (H ∩ M) 7 9
HR + Finance, n(H ∩ F) 6 7
Marketing + Finance, n (M ∩ F) 5 8
Marketing + Finance + HR, n (M ∩ F ∩ H) 2 3


Reqd ratio = 5 : 4
4
By what per cent is the number of of boys in Marketing discipline more than the number of girls in HR discipline? 
» Explain it
D
Boys =  7  × 150 = 70;  Girls =  8  × 150 = 80
15 15

Disciplines  Boy   Girl 
Marketing, n(M) 28 40
HR, n(M) 21 24
Finance, n(F) 21 16
HR + Marketing, n (H ∩ M) 7 9
HR + Finance, n(H ∩ F) 6 7
Marketing + Finance, n (M ∩ F) 5 8
Marketing + Finance + HR, n (M ∩ F ∩ H) 2 3



Reqd% =  28 – 24  × 100 =  4  × 100 = 16 2 %
24 24 3

5
The ratio of boys to girls enrolled only in HR discipline is
» Explain it
A
Boys =  7  × 150 = 70;  Girls =  8  × 150 = 80
15 15

Disciplines  Boy   Girl 
Marketing, n(M) 28 40
HR, n(M) 21 24
Finance, n(F) 21 16
HR + Marketing, n (H ∩ M) 7 9
HR + Finance, n(H ∩ F) 6 7
Marketing + Finance, n (M ∩ F) 5 8
Marketing + Finance + HR, n (M ∩ F ∩ H) 2 3



Reqd ratio = 10 : 11