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