The average of eighteen numbers is 42. The average of the last ten numbers is 40 and that of the first five numbers is 44. The seventh number is 6 less than the sixth and 7 less than the eighth number. The average of the sixth and the eighth number is:

47.5

Sum of 18 numbers is = 18 × 42 = 756

Sum of first 5 numbers is = 5 × 44 = 220

Sum  of last 10 numbers = 10 × 40 = 400

Sum of 6th , 7th & 8th number  = 756  - (220 + 400) = 136

Let seventh number = a , Then 6th number = a + 6   & 8th number = a + 7 

ATQ ,

a + a + 6 + a + 7 = 136

3a = 123

a = 41

6th number = 41 + 6 = 47  & 8th number = 41 + 7 = 48

Average of 6th and 8th number = \(\frac{47 + 48 }{2}\)  = 47.5