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 12th number is 6 less than the 13th number. What is the average of the 11th and the 13th numbers?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 87
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Understanding |
Application |
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Given: Average of 13 numbers = 80 The average of the first 5 numbers = 74.5 And Average of next 5 numbers = 82.5 Suppose 12th number = x Then 11th number = x + 6 13th number = x + 6 |
Sum of 13 number = 13 x 80 = 1040 Sum of first five number = 5 x 74.5 = 372.5 Sum of next five number = 5 x 82.5 = 412.5 Sum of first 10 number = 372.5 + 412.5 = 785 Now, sum of last three number = 1040 – 785 =255 According to question, x + 6 + x + x + 6 = 255 3x = 255 – 12 3x = 243 x = 81 11th number = 87 13th number = 87 Average = (87 + 87)/2 = 87 |