In a school there were 1582 students and the ratio of boys to girls was 4:3. After some days, 30 girls joined but a few boys left, and the ratio of boys to girls became 7:6. How many boys left the school?

The initial 1582 students in the ratio 4:3 give 904 boys and 678 girls, since one part equals 1582 divided by 7, that is 226.

After 30 girls join, the number of girls becomes 678 plus 30, which is 708.

The new ratio of boys to girls is 7:6, so boys equal 708 multiplied by 7 and divided by 6, which is 826.

The number of boys who left is 904 minus 826, which is 78.

The girls' count is used as the fixed known value to solve for the reduced boys' count.

Ratio problems are solved by first converting each part into an actual number using the total.