Question

The average of eleven numbers is 20 and the average of the first five numbers is 22, while the average of the last five numbers is 18. What is the sixth number? ​

Answer 1

Answer:

The sixth number = 20

Given:

• The average of 11 numbers = 20
• The average of first 5 numbers = 22
• The average of last 5 numbers = 18

To Find:

• The sixth Number.

Solution:

Sum of all the 11 numbers:

⟹ Average of numbers × Total numbers

⟹ 20 × 11

⟹ 220

Sum of first 5 numbers:

⟹ Average of numbers × Total numbers

⟹ 22 × 5

⟹ 110

Sum of last 5 numbers:

⟹ Average of numbers × Total numbers

⟹ 18 × 5

⟹ 90

[ We have sum of all numbers and sum of numbers without the 6th number, so we can find the 6th number by finding the difference between Sum of all numbers and sum of numbers without 6th number ]

Sixth Number =

⟹ {Sum of all numbers - ( Sum of first 5 numbers + Sum of last 5 numbers }

⟹ 220 - ( 110 + 90 )

⟹ 220 - 200

⟹ 20

The sixth number = 20

Answer 2

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Given:

The average of 11 numbers = 20

The average of first 5 numbers = 22

The average of last 5 numbers = 18

To Find:

The sixth Number.

Solution:

Sum of all the 11 numbers:

⟹ Average of numbers × Total numbers

⟹ 20 × 11

⟹ 220

Sum of first 5 numbers:

⟹ Average of numbers × Total numbers

⟹ 22 × 5

⟹ 110

Sum of last 5 numbers:

⟹ Average of numbers × Total numbers

⟹ 18 × 5

⟹ 90

Sixth Number =

⟹ {Sum of all numbers - ( Sum of first 5 numbers + Sum of last 5 numbers }

⟹ 220 - ( 110 + 90 )

⟹ 220 - 200

⟹ 20

The sixth number = 20