In a school the total number of students was 350 and the ratio of the number of boys and girls was 4: 3. After a few days 30 girls joined the school but a few boys left, as a result the ratio of the boys and the girls became 5: 6. Find the number of boys who left the school.35402550

Sure, let's solve this step by step:

Step 1: We know the total number of students was 350 and the ratio of boys to girls was 4:3. This means the total ratio representing the students is 4+3 = 7.

Step 2: To find the number of boys and girls, we divide the total number of students by the total ratio. So, 350/7 = 50. This means each unit of the ratio represents 50 students.

Step 3: Therefore, initially, the number of boys was 450 = 200 and the number of girls was 350 = 150.

Step 4: After a few days, 30 girls joined the school, increasing the number of girls to 150+30 = 180.

Step 5: At this point, the ratio of boys to girls became 5:6. This means the total ratio representing the students is now 5+6 = 11.

Step 6: We know that each unit of the ratio represents the same number of students, so we can set up the equation 5x = number of boys and 6x = number of girls (180). Solving for x gives us x = 180/6 = 30.

Step 7: Therefore, the number of boys at this point was 5*30 = 150.

Step 8: Since we know the initial number of boys was 200, the number of boys who left the school is 200 - 150 = 50.

So, 50 boys left the school.