In a class, boys : girls = 4 : 5 initially. If 10 more boys join, the new ratio becomes 6 : 5. How many girls are there in the class?

Introduction / Context: This problem uses initial ratio and a post-change ratio after a fixed increment to one group to find the original scale and the number of girls.

Given Data / Assumptions: Boys : Girls = 4 : 5 initially; after 10 boys join → 6 : 5.

Concept / Approach: Express boys and girls as 4x and 5x; add 10 to boys and set the ratio to 6 : 5; solve for x, then compute girls.

Step-by-Step Solution: Initial: B = 4x, G = 5x. After joining: (4x + 10) / 5x = 6 / 5. Cross-multiply: 5(4x + 10) = 6(5x) ⇒ 20x + 50 = 30x ⇒ 10x = 50 ⇒ x = 5. Girls = 5x = 25.

Verification / Alternative check: Boys initially 20; after +10 → 30; ratio 30 : 25 = 6 : 5; consistent.

Why Other Options Are Wrong: 20, 30, 35 do not satisfy both the initial and final ratio conditions.

Common Pitfalls: Adding 10 to both groups or misapplying the ratio after the change.

Final Answer: 25