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 6$$^{th}$$ number is 6 less than the fifth and 5 less than the 7$$^{th}$$ number. The average of the 5$$^{th}$$ and the 7$$^{th}$$ numbers is:

Average of twelve numbers = 42

Sum of twelve numbers = 42 $$\times$$ 12 = 504

Average of the last five numbers = 40

Sum of the last five numbers = 200

Average of first four numbers = 44

Sum of first four numbers =176

Sum of 5th , 6th and 7th term = 504 - 200 -176 = 128

Now , lets suppose 6th term is x.

5th term would be (x+6) and 7th term would be (x+5).

x+5 +x + x+6 =128

x=39

6th term = 45 & 7th term = 44

Average of 6th & 7th term = $$\frac{89}{2}$$ = 44.5