The average of sixteen numbers is 48. The average of the first six of these numbers is 45 and that of the last seven numbers is 53. The seventh and the eighth numbers are, respectively, 3 and 7 greater than the ninth number. What is the average of the ninth and seventh numbers?

40.5

Sum of sixteen numbers = 48 x 16 = 768

Sum of 1st six numbers = 45 x 6 = 270

Sum of last seven numbers = 7 x 53 = 371

Lets assume 9th number be x

                   7th number = x + 3

                   8th number = x + 7

Sum of 7th, 8th and 9th numbers = 768 - 270 - 371 = 127

⇒ x + 3 + x + 7 + x = 127

⇒ x = 39

Average of 9th and 7th number = \(\frac{39 + 42}{2}\) = 40.5