Q7. Average of 60 numbers are 55. When 10 more numbers are included, the average of 70 numbers become 75. Find the
average of 10 numbers.

The average of the 10 numbers is 195

Step-by-step explanation:

The average of a set of numbers is the sum of the numbers dividing by their number

∵ The average of 60 numbers is 55

∴ The average = 55

∴ The number = 60

→ Substitute them in the rule above to find the sum of the numbers

∵ 55 = The sum ÷ 60

→ Multiply each side by 60

∴ 3300 = The sum

∴ The sum of the 60 numbers = 3300

∵ 10 more numbers are included

∵ The average of  70 numbers become 75

∴ The average = 75

∴ The number = 70

→ Substitute them in the rule above to find the sum of the numbers

∵ 75 = The sum ÷ 70

→ Multiply each side by 70

∴ 5250 = The sum

∴ The sum of the 70 numbers = 5250

∵ The sum of the 10 numbers that added is the difference between

   the sums of the 60 and 70 numbers

∵ The difference between the sums = 5250 - 3300

∴ The difference between the sums = 1950

→ To find the average of them divide their sum by 10

∵ The average of the 10 numbers = 1950 ÷ 10

∴  The average of the 10 numbers = 195