<p>Total number of students = 100, number of boys = 70, number of girls = 30. Mean of boys = 75 and combined mean = 72. Find the mean of girls.</p>
Step-by-Step Solution
Key Concept: Use the weighted average formula: combined mean = (n₁·x̄₁ + n₂·x̄₂)/(n₁ + n₂). Substitute known values and solve for the unknown mean algebraically.
<p><strong>Step 1:</strong> Set up the weighted average equation using the combined mean formula.</p><p>Combined mean = (n_boys × mean_boys + n_girls × mean_girls) / Total students</p><p><strong>Step 2:</strong> Substitute the known values: n_boys = 70, mean_boys = 75, n_girls = 30, combined mean = 72, total = 100</p><p>72 = (70 × 75 + 30 × mean_girls) / 100</p><p><strong>Step 3:</strong> Multiply both sides by 100:</p><p>7200 = 5250 + 30 × mean_girls</p><p><strong>Step 4:</strong> Solve for mean_girls:</p><p>30 × mean_girls = 7200 - 5250 = 1950</p><p>mean_girls = 1950 / 30 = 65</p><p>∴ Answer: B (Mean of girls = 65)</p>
Correct Answer: B