In a school there were 1776 students and the ratio of the number of boys and girls was 5 : 3. After a few months 34 girls joined but few boys left. As a result the ratio becomes 11 : 7. Find the number of boys who left the school.

In a school there were 1776 students and the ratio of the number of boys and girls was 5 : 3. After a few months 34 girls joined but few boys left. As a result the ratio becomes 11 : 7. Find the number of boys who left the school. Correct Answer 10

Given:

Initially, the number of students was 1776

Initial ratio of boys and girls is 5 : 3

34 girls joined and few boys left

Final ratio of boys and girls is 11 : 7

Concept:

As the number of students given and ratio is also given. From here we can find the number of boys and girls.

Calculation:

Let the initial number of boys and girls be 5x and 3x

Let the number of boys left the school be y

Given that 5x + 3x = 1776

⇒ 8x = 1776

⇒ x = 222

Number of boys initially = 5x = 1110

Number of girls initially = 3x = 666

Final number of girls = 666 + 34 = 700

Now,

(1110 – y)/700 = 11/7

⇒ y = 10

It means 10 boys left the school.

Alternate Method:

Given ratio = 5 : 3

⇒ 8R = 1776

⇒ R = 222

Number of boys = 5R = 1110

Number of girls = 3R = 666

Now,

34 girls added

New number of girls = 700

Final ratio of boys and girls = 11 : 7

Now, 7Q = 700

⇒ 1Q = 100

New number of boys = 11 × 100 = 1100