The sum of 10 numbers is 490. If the average of their first 4 numbers is 53 and that of the last five is 42, then what is the 5^th number?

Question: The sum of 10 numbers is 490. If the average of their first 4 numbers is 53 and that of the last five is 42, then what is the 5^th number?

Solution:
Given,
the average of their first 4 numbers = 53
∴ The total of their first 4 numbers = 4 × 53 = 212
and,
the average of their last five = 42
The total of the last 5 numbers = 5 × 42 = 210

∴ The sum of the (4 + 5) = 9 numbers = (212 + 210) = 422

∴ The 5^th number = 490 - 422 = 68