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      Question

      The average of 18 numbers is 75.

      The average of the first nine numbers and the last six numbers is 62.5 and 82.5, respectively. The 12th number is 34.3 more than 1.8 times the 10th number, which itself is 119.5 less than the 11th number. What is the value of the 11th number?
      A 120 Correct Answer Incorrect Answer
      B 165 Correct Answer Incorrect Answer
      C 156 Correct Answer Incorrect Answer
      D 250 Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let 10th number is ‘x’ So, 12th number = 1.8 × x + 34.3 And, 11th number = x + 119.5 So, x + 1.8x + 34.3 + x + 119.5 = 18 × 75 – 9 × 62.5 – 6 × 82.5 = 292.5 Or, 3.8x = 138.7 Or, x = 36.5 So, 11th number = 36.5 + 119.5 = 156

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