The ratio of the number of boys and girls in a hostel is 5 : 7. If 40% of boys and 50% of girls are getting scholarships for their studies, what is the percentage of hostel students who are not getting any scholarships?

Correct option is B

Given:

Ratio of boys to girls = 5:7

Let the number of boys = 5x and the number of girls = 7x

Percentage of boys getting scholarships = 40%

Percentage of girls getting scholarships = 50%

Formula Used:

Total students = Boys + Girls

Students getting scholarships = (Percentage of boys with scholarships × Total boys) + (Percentage of girls with scholarships × Total girls)

Percentage of students not getting scholarships = $$100\% - \left(\frac{\text{Students getting scholarships}}{\text{Total students}} \times 100\%\right)$$​

Solution:

Total students = 5x + 7x = 12x

Students getting scholarships:

(40% × 5x) + (50% × 7x)

= 2x + 3.5x

= 5.5x

Percentage of students getting scholarships

$$\frac{5.5x}{12x} \times 100\\ \ \\= \frac{5.5}{12} \times 100$$ 

= $$\frac{550}{12}$$ $$\frac{325}6$$​​

= $$\frac{275}6$$​% 

Percentage of students not getting scholarships

100% − $$\frac{275}6$$​%

= $$\frac{600-275}6$$ 

= $$\frac{325}6$$ 

= 54$$\frac16$$%​