The average ofnnumbers is45. If60%of the numbers are increased by5each and the remaining numbers are decreased by10each, then what is the average of the numbers so obtained?a)42b)43c)46d)44Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Given,
The average of n numbers is 45.
60% of the numbers are increased by 5.
The remaining numbers are decreased by 10 each.
As we know,

Let the n number be 100 and their average is 45.
The average increases by 5 for 60% of numbers
New average =(45+5)=50
Sum =60% of 100 x 50

= Rs. 3,000
For the remaining 40% average decreased by 10 each.
New average =45−10
=35
Sum =40% of 100 x 35

= Rs. 1,400
Now,

= 44
∴ The required average is 44.

Answer

Let's assume that we have n numbers whose average is 45.

Step 1: Finding the sum of the n numbers
Since the average of n numbers is 45, the sum of the n numbers can be calculated by multiplying the average (45) by the total count of numbers (n).
Sum of n numbers = Average * Total count = 45 * n

Step 2: Increasing 60% of the numbers by 5
To find the count of numbers that need to be increased, we multiply the total count (n) by the percentage (60%) and divide it by 100.
Count of numbers to be increased = (60/100) * n = 0.6n

Now, we can calculate the new sum by increasing the selected numbers by 5. Since the count of these numbers is 0.6n, the increase in sum will be (0.6n * 5).

Step 3: Decreasing the remaining numbers by 10
To find the count of numbers that need to be decreased, we subtract the count of numbers to be increased (0.6n) from the total count (n).
Count of numbers to be decreased = n - 0.6n = 0.4n

Now, we can calculate the decrease in sum by multiplying the count of these numbers (0.4n) by 10 (-10).

Step 4: Calculating the new average
To find the new average, we need to calculate the new sum of the numbers and divide it by the total count (n).

New sum = Sum of increased numbers + Sum of decreased numbers
= (45 * n) + (0.6n * 5) + (0.4n * -10)
= 45n + 3n - 4n
= 44n

New average = New sum / Total count
= 44n / n
= 44

Therefore, the average of the numbers after increasing 60% of them by 5 and decreasing the remaining numbers by 10 is 44. Hence, the correct answer is option D) 44.

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