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      Question

      The average marks of 'm' students in a math test is (m +

      5) and the average marks of 30 girls is (2m - 10). If the average marks of all students together is 55, then find the number of boys.
      A 75 Correct Answer Incorrect Answer
      B 55 Correct Answer Incorrect Answer
      C 25 Correct Answer Incorrect Answer
      D 45 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      [m × (m + 5) + 30 × (2m - 10)] ÷ (m + 30) = 55 ⇒ m² + 5m + 60m - 300 = 55m + 1650 ⇒ m² + 5m + 5m - 1950 = 0 ⇒ m² + 10m - 1950 = 0 ⇒ m² + 65m - 55m - 1950 = 0 ⇒ m(m + 65) - 55(m + 65) = 0 ⇒ (m + 65)(m - 55) = 0 So, m = 55 or -65 Number of boys cannot be negative ∴ m = 55

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