The average of 8 numbers is 30. The average of the first 2 numbers is 26 and that of the next three is 28. The sixth number is less than the seventh by 3 and less than the eighth by 5. Find the eighth number.

The eighth number is 37.

total of 8 numbers = 8 x 30 = 240.

first 2 sum = 52, next 3 sum = 84, together 136.

last three sum = 240 - 136 = 104.

with 6th = x, 7th = x+3, 8th = x+5: 3x + 8 = 104.

x = 32, so 8th = 32 + 5 = 37.