Twenty girls and y boys sat on an examination. The mean marks obtained by the girls and boys were 52 and 57…

Analyze the question: We're given the number of girls (20), the number of boys (y), their mean marks (52 and 57), and the combined total score (2750). We need y.

Concept: Mean = Total score ÷ Number of students, so Total score = Mean × Number of students.

Solution:

• Girls' total = 20 × 52 = 1040
• Boys' total = 57 × y = 57y
• Combined total: 1040 + 57y = 2750

57y = 2750 − 1040 = 1710

y = 1710 ÷ 57 = 30

Check: Boys' total = 30 × 57 = 1710. Then 1040 + 1710 = 2750 ✓

Tip: In "mean" problems, always convert to totals first (Total = Mean × Number). Then the problem becomes a simple linear equation. Always check by substituting back, since it takes only seconds.