The average of 24 numbers is 65. The average of first 11 numbers is 67 and the average of last 10 numbers is 70. If the 12th number is 13 less than the 13th number, and the 14th number is one more than the 13th number, then the average of 12th and 14th number is –

Total sum = 24 × 65 = 1560. Sum of first 11 = 11 × 67 = 737. Sum of last 10 = 10 × 70 = 700. Sum of positions 12, 13, 14 = 1560 - 737 - 700 = 123. Let 13th number = x. Then 12th = x - 13, 14th = x + 1. So (x-13) + x + (x+1) = 123, giving 3x - 12 = 123, so 3x = 135, x = 45. Average of 12th and 14th = (32 + 46)/2 = 78/2 = 39. This tests weighted average concepts and algebraic reasoning.