The ratio of the number of boys and girls in a school is 5:9 and the total number of students is 224. If 64 girls left the school and some boys joined the ratio becomes 6 : 5. Find the number boys who joined.

Step 1: Find the total number of boys and girls in the school initially.

The ratio of boys to girls is 5:9, and the total number of students is 224.

So, the total parts in the ratio = 5 (for boys) + 9 (for girls) = 14 parts.

Each part is therefore equal to 224/14 = 16 students.

Step 2: Find the initial number of boys and girls.

The number of boys = 5 parts * 16 = 80 boys. The number of girls = 9 parts * 16 = 144 girls.

Step 3: Adjust for the girls who left and the new ratio.

64 girls left the school, so the new number of girls = 144 - 64 = 80 girls.

The new ratio of boys to girls is 6:5. Since we know the number of girls is 80, each part in this new ratio is equal to 80/5 = 16 students.

Step 4: Find the new number of boys.

The new number of boys = 6 parts * 16 = 96 boys.

Step 5: Find the number of boys who joined.

The number of boys who joined = The new number of boys - The initial number of boys = 96 - 80 = 16 boys.

So, 16 boys joined the school.