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In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If the number of boys participating in the sports is 15, then how many girls are there in the class?

In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If the number of boys participating in the sports is 15, then how many girls are there in the class? Correct Answer 30

Given:

Total number of students in the class = 60

The ratio of number of boys and girls participating in the annual sports = 3 : 2

The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports

The number of boys participating in the sports = 15

Concept:

At first, finding the number of girls and boys participating in the annual sports. Then subtracting from total number of students to get the number of boys and girls not participating in the annual sports.

Calculation:

Let the number of boys and girls participating in the annual sports be 3x and 2x respectively

And the number of boys and girls not participating in the annual sports be y and (y + 5) respectively

The number of boys participating in the sports = 15

⇒ 3x = 15

⇒ x = 5

The number of girls participating in annual sports = 2x

⇒ 2 × 5 = 10

∴ The total number of students participating in annual sports = 15 + 10 = 25

Now, Total number of students in the class = 60

⇒ 25 + y + (y + 5) = 60

⇒ 2y + 30 = 60

⇒ 2y = 30

⇒ y = 15

The number of girls not participating in annual sports = y + 5 

⇒ 15 + 5 = 20

∴ Total number of girls = The number of girls participating in annual sports + The number of girls not participating in annual sports

⇒ 10 + 20 = 30

∴ Total number of girls in the class = 30

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