Multiple choice

The average of thirteen numbers is 80. The average of the first five numbers is 74.5 and that of the next five numbers is 82.5. The 11th number is 6 more than the 12th number and the 12th number is 6 less than the 13th number. What is the average of the 11th and 13th numbers?

  1. $87$
  2. $54$
  3. $85$
  4. $86$
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A Correct answer
Explanation

Total sum = 13 × 80 = 1040. Sum of first 10 numbers = 5 × 74.5 + 5 × 82.5 = 372.5 + 412.5 = 785. Sum of 11th, 12th, 13th = 1040 - 785 = 255. Let 12th = x, then 11th = x + 6, 13th = x + 6. So (x + 6) + x + (x + 6) = 255, giving 3x = 243, x = 81. Average of 11th and 13th = (87 + 87)/2 = 87.

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