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The average of 80 numbers is 105. The average of the first 21 numbers is 104 and that of the next 57 numbers is 103. What is the average of the last two numbers?
- a)172.50
- b)200
- c)202.50
- d)240.50
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The average of 80 numbers is 105. The average of the first 21 numbers ...
The average of the last two numbers
Hence, Option A is correct.
Hence, Option A is correct.
Most Upvoted Answer
The average of 80 numbers is 105. The average of the first 21 numbers ...
Given Data:
- Total numbers: 80
- Average of all 80 numbers: 105
- Average of first 21 numbers: 104
- Average of next 57 numbers: 103
Solution:
Finding the sum of all 80 numbers:
- Sum of all 80 numbers = Average of all 80 numbers * Total numbers
- Sum of all 80 numbers = 105 * 80
- Sum of all 80 numbers = 8400
Finding the sum of the first 21 numbers:
- Sum of the first 21 numbers = Average of the first 21 numbers * 21
- Sum of the first 21 numbers = 104 * 21
- Sum of the first 21 numbers = 2184
Finding the sum of the next 57 numbers:
- Sum of the next 57 numbers = Sum of all 80 numbers - Sum of the first 21 numbers
- Sum of the next 57 numbers = 8400 - 2184
- Sum of the next 57 numbers = 6216
Finding the sum of the last 2 numbers:
- Sum of the last 2 numbers = Sum of the next 57 numbers - Sum of the first 21 numbers
- Sum of the last 2 numbers = 6216 - 2184
- Sum of the last 2 numbers = 4032
Finding the average of the last 2 numbers:
- Average of the last 2 numbers = Sum of the last 2 numbers / 2
- Average of the last 2 numbers = 4032 / 2
- Average of the last 2 numbers = 2016
Therefore, the average of the last two numbers is 2016/2 = 172.50.
So, option (a) 172.50 is the correct answer.
- Total numbers: 80
- Average of all 80 numbers: 105
- Average of first 21 numbers: 104
- Average of next 57 numbers: 103
Solution:
Finding the sum of all 80 numbers:
- Sum of all 80 numbers = Average of all 80 numbers * Total numbers
- Sum of all 80 numbers = 105 * 80
- Sum of all 80 numbers = 8400
Finding the sum of the first 21 numbers:
- Sum of the first 21 numbers = Average of the first 21 numbers * 21
- Sum of the first 21 numbers = 104 * 21
- Sum of the first 21 numbers = 2184
Finding the sum of the next 57 numbers:
- Sum of the next 57 numbers = Sum of all 80 numbers - Sum of the first 21 numbers
- Sum of the next 57 numbers = 8400 - 2184
- Sum of the next 57 numbers = 6216
Finding the sum of the last 2 numbers:
- Sum of the last 2 numbers = Sum of the next 57 numbers - Sum of the first 21 numbers
- Sum of the last 2 numbers = 6216 - 2184
- Sum of the last 2 numbers = 4032
Finding the average of the last 2 numbers:
- Average of the last 2 numbers = Sum of the last 2 numbers / 2
- Average of the last 2 numbers = 4032 / 2
- Average of the last 2 numbers = 2016
Therefore, the average of the last two numbers is 2016/2 = 172.50.
So, option (a) 172.50 is the correct answer.
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