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The average of 13 numbers is 57. The average of the first three numbers is 8 less than that of 13 numbers and the next seven numbers is 2 more than that of 13 numbers. The 11th number is two times the 12th number and 12th number is 1 less than the 13th number. What is the average of 11th and 12th numbers?

The average of 13 numbers is 57. The average of the first three numbers is 8 less than that of 13 numbers and the next seven numbers is 2 more than that of 13 numbers. The 11th number is two times the 12th number and 12th number is 1 less than the 13th number. What is the average of 11th and 12th numbers? Correct Answer 67.5

Given:

The average of 13 numbers = 57

The average of the first three numbers is 8 less than that of 13 numbers

The average of the next seven numbers is 2 more than that of 13 numbers

The 11th number is two times the 12th number

12th number is 1 less than the 13th number

Formula Used:

Average = Sum of observations/Number of observations

Calcualtion:

Let 11th number be 2x,

12th number = x

13th number = x + 1

The average of 13 numbers = 57

Sum of 13 numbers = 57 × 13 = 741

Average of first three numbers = 57 – 8 = 49

Sum of first three numbers = 49 × 3 = 147

Average of next seven numbers = 57 + 2 = 59

Sum of next seven numbers = 59 × 7 = 413

Sum of 11th, 12th and 13th numbers = 741 – 147 – 413 = 181

⇒ 2x + x + x + 1 = 181

⇒ 4x + 1 = 181

⇒ 4x = 181 – 1

⇒ x = 180/4 = 45

⇒ 11th number = 2x = 2 × 45 = 90

⇒ 12th number = 45

Sum of 11th number and 12th number = 90 + 45 = 135

∴ Average of 11th and 12th number = 135/2 = 67.5

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