The average of 16 numbers is 64. The average of the first 7 numbers is 61 and the average of the next 6 numbers is 68. If the 14th numbers is 13 less than the 15th number and is 7 more than 16th number, then the average of the 15th and 16th number is?

64

Let 15th number = x, then 14th = x - 13 and 16th = x -20

Now ATQ,

⇒ (7 × 61) + (6 × 68) + (3x - 33) = (16 × 64)

⇒ 427 + 408 + 3x - 33 = 1024

⇒ 3x + 802 = 1024

⇒ 3x = 222

⇒ x = 74,

Hence, 15th number = 74 and  16th = 74 - 20 = 54

Therefore,

⇒ Average of 15th and 16th number = \(\frac{74 + 54}{2}\) = 64