Question

The ratio of the number of boys and girls in a school is 3 ∶ 2. If 20% of the boys and 25% of the girls are Scholarship holders, what fraction of the students do not get the scholarship?
1. \(\dfrac{39}{50}\)
2. \(\dfrac{2}{3}\)
3. \(\dfrac{75}{100}\)
4. \(\dfrac{63}{75}\)
5.

Answer 1

Correct Answer - Option 1 : \(\dfrac{39}{50}\)

Given:

Ratio of number of boys and girls in school = 3 ∶ 2

Scholarship holding boys = 20%

Scholarship holding girls = 25%

Formula used:

Fraction of student who does not get scholarship = Number of students who do not get scholarship / Total number of students in the school

Calculations:

Let the total number of students in the school be 100x

Number of boys in the school = (3/5) × 100x

⇒ 60x

Number of girls in the school = (2/5) × 100x

⇒ 40x

Number of boys with scholarship = (20/100) × 60x 

⇒ 12x

Number of girls with scholarship = (25/100) × 40x 

⇒ 10x

Number of students who do not get scholarship = 100x - (12x + 10x)

⇒ 100x - 22x

⇒ 78x

Fraction of students who do not get scholarship = (78x)/(100x)

⇒ 39/50

∴ The fraction of students who do not get a scholarship is \(\dfrac{39}{50}\)