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      Question

      The average age of 'p' employees

      in the HR department is (p – 6) years. Two managers aged 36 and 40 join the department, causing the overall average age in HR to rise by 2 years. In the IT department, there are (p + 35) employees, and 25% of them are women. The average age of each woman is 14 years, and the average age of each man is 16 years. Find the average age of an employee in the IT department.
      A 15.5 yrs Correct Answer Incorrect Answer
      B 22.5 yrs Correct Answer Incorrect Answer
      C 18.5 yrs Correct Answer Incorrect Answer
      D 28.5 yrs Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      We have the equation: p × (p – 6) + 36 + 40 = (p + 2) × (p – 6 + 2) Simplifying: p² – 6p + 76 = p² + 2p – 4p – 8 So, 76 + 8 = –2p + 6p 4p = 84 p = 21 Number of employees in the HR department = 21 Number of employees in the IT department = p + 35 = 56 years Number of women in IT = 0.25 × 56 = 14 years Number of men in IT = 56 – 14 = 42 years Required average age = {(14 × 14) + (42 × 16)}/56 = (196 + 672)/56 = 868/56 = 15.5 years

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