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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