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The average of n numbers is 41. If two-thirds of the numbers are increased by 9 and the remaining are decreased by 6, find the new average.
- a)36
- b)39
- c)42
- d)45
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The average of n numbers is 41. If two-thirds of the numbers are incre...
Total of n numbers = 41n
If two thirds of the numbers are increased by 9, the total increases by (2n/3) × 9
If the remaining are decreased by 6, the total goes down by (n/3) × 6
The new total = 41n + (2n/3) × 9 – (n/3) × 6 = 45n
∴ new average = 45n/n = 45
∴ new average = 45n/n = 45
Most Upvoted Answer
The average of n numbers is 41. If two-thirds of the numbers are incre...
Let's assume that there are n numbers whose average is 41.
To find the new average, we need to calculate the sum of the new numbers and divide it by the total count of numbers.
Let's break down the problem into two parts:
1. Two-thirds of the numbers are increased by 9:
- Since two-thirds of the numbers are increased by 9, we can calculate the sum of these numbers.
- Let's assume that there are x numbers out of n that are increased by 9.
- The sum of these numbers would be x * 9 (as each number is increased by 9).
2. The remaining numbers are decreased by 6:
- Since the remaining numbers are decreased by 6, we can calculate the sum of these numbers.
- The count of remaining numbers would be n - x (as x numbers were increased by 9).
- The sum of these numbers would be (n - x) * (-6) (as each number is decreased by 6).
Now, let's calculate the new sum:
New Sum = Sum of increased numbers + Sum of decreased numbers
= (x * 9) + ((n - x) * (-6))
= 9x - 6(n - x)
= 9x - 6n + 6x
= 15x - 6n
The new average can be calculated by dividing the new sum by the total count of numbers:
New Average = New Sum / Total count of numbers
= (15x - 6n) / n
Since we are looking for the new average, the correct option is D) 45, as the average is equal to the new sum divided by the total count of numbers.
To find the new average, we need to calculate the sum of the new numbers and divide it by the total count of numbers.
Let's break down the problem into two parts:
1. Two-thirds of the numbers are increased by 9:
- Since two-thirds of the numbers are increased by 9, we can calculate the sum of these numbers.
- Let's assume that there are x numbers out of n that are increased by 9.
- The sum of these numbers would be x * 9 (as each number is increased by 9).
2. The remaining numbers are decreased by 6:
- Since the remaining numbers are decreased by 6, we can calculate the sum of these numbers.
- The count of remaining numbers would be n - x (as x numbers were increased by 9).
- The sum of these numbers would be (n - x) * (-6) (as each number is decreased by 6).
Now, let's calculate the new sum:
New Sum = Sum of increased numbers + Sum of decreased numbers
= (x * 9) + ((n - x) * (-6))
= 9x - 6(n - x)
= 9x - 6n + 6x
= 15x - 6n
The new average can be calculated by dividing the new sum by the total count of numbers:
New Average = New Sum / Total count of numbers
= (15x - 6n) / n
Since we are looking for the new average, the correct option is D) 45, as the average is equal to the new sum divided by the total count of numbers.
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The average of n numbers is 41. If two-thirds of the numbers are increased by 9 and the remaining are decreased by 6, find the new average.a)36b)39c)42d)45Correct answer is option 'D'. Can you explain this answer?
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