The average of thirteen numbers is 47. The average of the tirst three numbers is 39 and that of next seven numbers is 49. The $$11^{th}$$ number is two times the $$12^{th}$$ number and $$12^{th}$$ number is 3 less then the $$13^{th}$$ number. What is the average of $$11^{th}$$ and $$13^{th}$$ numbers?

The average of thirteen numbers = 47
Sum of thirteen numbers = 47 $$\times$$ 13 = 611
The average of the first three numbers = 39
Sum of the first three numbers = 39 $$\times$$ 3 = 117
The average of the next seven numbers = 49
Sum of the next seven numbers = 49 $$\times$$ 7 = 343
11th number = 2 $$\times$$ 12th number
12th number = 13th number - 3
Sum of thirteen numbers = 611
Sum of the first three numbers + Sum of the next seven numbers + 11th number + 12th number + 13th number = 611
117 + 343 + 2 $$\times$$ 12th number + 12th number + 12th number + 3 = 611
4 $$\times$$ 12th number = 151 - 3
12th number = 148/4 = 37
11th number = 2 $$\times$$ 37 = 74
13th number = 37 + 3 = 40
Average of $$11^{th}$$ and $$13^{th}$$ numbers = $$\frac{74 + 40}{2} = \frac{114}{2} = 57$$
$$\therefore$$ The correct answer is option B.