The average of fourteen numbers is 46. The average of first five is $43 and that of last six numbers is 49.5. The sixth and seventh numbers are respectively 4 and 8 greater than the eighth number. What is the average of sixth and seventh numbers?

Sum of all 14 numbers = 14×46=644
Sum of first 5 numbers = 5×43=215
Sum of last 6 numbers = 6×49.5=297

Sum of the remaining numbers (6th, 7th, and 8th numbers):

Sum
6,7,8
​
=644−(215+297)=644−512=132
Let the 8th number be z.
According to the problem:

6th number=z+4
7th number=z+8
Thus:

(z+4)+(z+8)+z=132
3z+12=132
3z=120⟹z=40
Now, find the 6th and 7th numbers:

6th number=40+4=44
7th number=40+8=48
Average of the 6th and 7th numbers:

Average=
2
44+48
​
=
2
92
​
=46