At a workshop, the ratio of boys to girls was 3 : 5. After 6 more boys joined and 4 girls left, the ratio became 5 : 6. How many boys were at the workshop in the end?
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Worked Solution
Step 1: Let initial boys = 3u and initial girls = 5u.
Step 2: After the change: boys = 3u + 6, girls = 5u − 4. New ratio gives (3u + 6) : (5u − 4) = 5 : 6.
Step 3: Cross-multiply: 6(3u + 6) = 5(5u − 4) → 18u + 36 = 25u − 20.
Step 4: Solve: 25u − 18u = 36 + 20 → 7u = 56 → u = 8.
Step 5: Final number of boys = 3u + 6 = 3(8) + 6 = 30.
Answer: 30
Correct answer: 30
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