Question

At a college in New Delhi $60$% of the students are boys and the rest are girls. Further, $15$% of the boys and $7.5$% of the girls are getting a fee waiver. The number of students getting a fee waiver is $90.$ Find the total number of students getting $50$% concession if it is given that $50$% of those not getting a fee waiver are eligible to get half fee concession?

• A. $360$
• B. $280$
• C. 320
• D. 330

Answer 1

The correct option is D 330

Let the total number of students=x.

Then, by the given data,

the number of boys=$x\times \frac{60}{100}=\frac{3x}{5}$.

So the number of girls=$x-\frac{3x}{5}=\frac{2x}{5}$.

15% of the boys=$\frac{3x}{5}\times \frac{15}{100}=\frac{9x}{100}$ boys get fee weiver.

7.5% of the girls= $\frac{2x}{5}\times \frac{7,5}{100}=\frac{3x}{100}$ girls get fee weiver.

$\therefore$ The total number of students getting fee weiver

=$\frac{9x}{100}+\frac{3x}{100}=\frac{3x}{25}$.

$\therefore$ By the given condition,

$\frac{3x}{25}=90⟹x=750$

which is the total number of the students.

So, the number of students, not getting fee will be

$=750-90=660$.

Now 50% of 660 students get half fee concession.

$\therefore$ their number=$660\times \frac{50}{100}=330$.

So the number of the students who get 50% fee concession $=330$.

Ans- Option D.