In a class, the ratio of the number of boys to that of girls is 3 : 5. The number of students who passed to that of who failed is 7 : 3. Among boys, the number of those who passed to those who failed is in the ratio 2 : 1. Among girls, what is the ratio of the number of girls who passed to those who failed?

Correct option is C

​Given:

Ratio of boys to girls = 3:5

Ratio of passed to failed students = 7:3

Among boys, ratio of passed to failed = 2:1

Solution: 

Total number of students = Sum of number of Boys + Girls = Sum of Passed + failed students 

Let total students = LCM of (3 + 5) and (7 + 3) = LCM(8, 10) = 40

Total boys and girls:

Boys = $$\frac{3}{8} \times 40$$​ = 15

Girls = $$\frac{5}{8} \times 40$$​ = 25

Passed and failed students:

Passed = $$\frac{7}{10} \times 40$$​ = 28

Failed = $$\frac{3}{10} \times 40$$​ = 12

Among boys (Passed : Failed = 2 : 1):

Total ratio parts = 2 + 1 = 3

Passed boys = $$\frac{2}{3} \times 15$$​ = 10

Failed boys = $$\frac{1}{3} \times 15$$​ = 5

Girls:

Passed girls = Total Passed – Passed Boys = 28 - 10 = 18

Failed girls = Total Failed – Failed Boys = 12 - 5 = 7

Now, Required Ratio:

Passed girls : Failed girls = 18 : 7