The average of 10 numbers is 60. The average of the first 5 numbers is 55 and the average of the next 3 numbers is 65. The 9th number is 10 less than the 10th number. Find the 10th number.

Question: The average of 10 numbers is 60. The average of the first 5 numbers is 55 and the average of the next 3 numbers is 65. The 9th number is 10 less than the 10th number. Find the 10th number.

Solution:
Total sum of 10 numbers = 10 × 60 = 600
Sum of first 5 numbers = 5 × 55 = 275
Sum of next 3 numbers (6th, 7th, and 8th) = 3 × 65 = 195

∴ Sum of first 8 numbers = 275 + 195 = 470
∴ Sum of 9th + 10th number = 600 - 470 = 130

Let the 10th number = x
Then, 9th number = x - 10
So,
(x - 10) + x = 130
⇒ 2x - 10 = 130
⇒ 2x = 140
⇒ x = 140/2
∴ x = 70

So, the 10th number is 70.