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### When 15 is included in a list of natural numbers, their mean is increased by 2. When 1 is included in this new list, the mean of the numbers in the new list is decreased by 1. How many numbers were there in the original list?

- A. 4
- B. 5
- C. 6
- D. 8

**Answer: Option A **

Here is complete explanation of When 15 is included in a list of natural numbers their….

__Solution(By ExamCraze Team)__

Let there be n numbers in the original list and let their mean be x.

Then, sum of n numbers = nx

$$eqalign{
& therefore frac{{nx + 15}}{{n + 1}} = x + 2 cr
& Rightarrow nx + 15 = left( {n + 1} right)left( {x + 2} right) cr
& Rightarrow nx + 15 = nx + 2n + x + 2 cr
& Rightarrow 2n + x = 13.....(i) cr} $$

And,

$$eqalign{
& therefore frac{{nx + 16}}{{n + 2}} = left( {x + 2} right) - 1 cr
& Rightarrow nx + 16 = left( {n + 2} right)left( {x + 1} right) cr
& Rightarrow nx + 16 = nx + n + 2x + 2 cr
& Rightarrow n + 2x = 14.....(ii) cr} $$

Solving (i) and (ii), we get:

n = 4, x = 5