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The average of 7 numbers is 43. If each number is decreased by 7, what will the new average be?
Question

The average of 7 numbers is 43. If each number is decreased by 7, what will the new average be?

A.

29

B.

36

C.

43

D.

7

Correct option is B

Given:

Number of values = 7

Original average = 43

Each number is decreased by 7

Formula Used:

Sum of numbers = Average ×\times​ Number of values

New Average=Sum of new numbersNumber of values\text{New Average} = \frac{\text{Sum of new numbers}}{\text{Number of values}}​​

Solution:

Sum of original numbers = Original average ×\timesNumber of values

Sum of original numbers = 43×\times7 = 301

Since each of the 7 numbers is decreased by 7, the total decrease in the sum is 7×\times 7 = 49.

Sum of new numbers = Sum of original numbers - Total decrease

Sum of new numbers = 301 - 49 = 252

New Average=Sum of new numbersNumber of values\text{New Average} = \frac{\text{Sum of new numbers}}{\text{Number of values}}​​

New average = 2527\frac{252 }{ 7}​ = 36

Therefore, the new average will be 36.

Alternative  Solution:

If each number in a set is decreased by the same value, the average will also decrease by that value.

New average = Original average - Decrease in each number

New average = 43 - 7 = 36

Option (B) is right.

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