Question : The ratio of the number of boys and girls in a school is 8 : 12. If 50% of boys and 25% of girls are getting scholarships for their studies, what is the percentage of school students who are not getting any scholarships?
Option 1: 65
Option 2: 66
Option 3: 67
Option 4: 68
Correct Answer: 65
Solution : Let the number of boys be $8x$. ⇒ The number of girls = $12x$ Total students $=8x+12x=20x$ According to the question, 50% of boys and 25% of girls are getting scholarships for their studies, ⇒ 50%(or $\frac12$) of the boys and 75%(or $\frac34$) of the girls are not getting the scholarship. 50% of Boys are not getting the scholarship. ⇒ $8x×\frac12=4x$ 75% of Girls are not getting the scholarship. ⇒ $12x × \frac34=9x$ $\therefore$ Percentage of students not getting the scholarship = $\frac{(4x+9x)}{20x}×100$ = 65% Hence, the correct answer is 65.
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