The average of twelve numbers is 42 . The average of the last five numbers is 40 , and that of the first four numbers is 44 . The sixth number is 6 less than the fifth number and 5 less than the seventh number. The average of the sixth and seventh numbers is:

41.5

Sum of 12 numbers = 12 x 42 = 504

Sum of last five numbers = 5 x 40 = 200

Sum of first four numbers = 4 x 44 = 176

Sum of 5th, 6th and 7th number = 504 - 200 - 176 = 130

Let 6th number be x

      5th number be x + 6

      7th number be x + 5

⇒ 3x + 11 = 128

⇒ x = 39

Average of 6th and 7th = \(\frac{39 + 44}{2}\) = 41.5