In an institute, 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. If the number of those getting a fee waiver is 90, find the total number of students getting 50% concessions if it is given that 50% of those not getting a fee waiver are eligible to get half fee concession?

In an institute, 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. If the number of those getting a fee waiver is 90, find the total number of students getting 50% concessions if it is given that 50% of those not getting a fee waiver are eligible to get half fee concession? Correct Answer 330

Let us assume there are 100 students in the institute. Then, number of boys = 60 And, number of girls = 40Further, 15% of boys get fee waiver = 9 boys7.5% of girls get fee waiver = 3 girlsTotal = 12 students who gets fee waiverBut, here given 90 students are getting fee waiver. So we compare12 = 90So, 1 = $$\frac{{90}}{{12}}$$ = 7.5Now number of students who are not getting fee waiver = 51 boys and 37 girls50% concession = 25.5 boys and 18.5 girls (i.e. total 44)Hence, required students = 44 × 7.5 = 330