Question
The average marks of 'n' boys is (n + 6) and that of 30
girls is (2n - 10). If the average marks of all students together is 52, find the number of boys.Solution
ATQ, [n × (n + 6) + 30 × (2n - 10)] ÷ (n + 30) = 52 Or, n² + 6n + 60n - 300 = 52n + 1560 Or, n² + 66n - 300 = 52n + 1560 Or, n² + 14n - 1860 = 0 Or, n² + 60n - 46n - 1860 = 0 Or, n(n + 60) - 31(n + 60) = 0 Or, (n + 60)(n - 31) = 0 So, 'n' = 31 or -60 Since number of boys cannot be negative, so 'n' = 31
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