The average of twelve numbers is 58. The average of the first five numbers is 56 and the average of the next four numbers is 60. The $10^{th}$ number is 4 more than the $11^{th}$ number and the $11^{th}$ number is one less than the $12^{th}$ number. What is the average of the $10^{th}$ and $12^{th}$ numbers?

59.5

Sum of 12 numbers = 12 x 58 = 696

Sum of 1st 5 numbers = 5 x 56 = 280

Sum of next 4 numbers = 4 x 60 = 240

Sum of 10th, 11th and 12th numbers = 696 - 280 - 240 = 176

Lets assume 12th number be x,

11th number = x - 1

10th number = x + 3

x + x - 1 + x + 3 = 176

3x = 174

x = 58

12th number = 58

10th number = 58 + 3 = 61

Average of 10th and 12th number = 59.5