The average of eleven numbers is 56. The average of first three numbers is 52 and that of next five numbers is 60. The 9th and 10th number are 3 and 1 more than the 11th number respectively. What is the average of 9th and 11th numbers ?

53.5

Lets assume 11th number be x

9th number = x + 3

10th number = x + 1

Sum of 11 numbers = 11 x 56 = 3 x 52 + 5 x 60 + x + 3 + x + 1 + x

⇒ 616 = 156 + 300 + 3a + 4

⇒ a = 52

11th number = 52

9th number = 52 + 3 = 55

10th number = 52 + 1 = 53

Average of 9th and 11th numbers = \(\frac{55 + 52}{2}\) = 53.5