Finding no. of items in the observation, when mean is given?

Question

The mean of certain number of observations is 40. If two more items with values 50 and 64 are added to this data, the mean increases to 42. Find the number of items in the original data?

Answer 1

Take $x$ to be the new number of items. Your grand total now is $42x$ (mean $\times$ number of items). The old total was $40(x-2)$ using the same logic. So you can write:

$42x = 40(x - 2) + 50 + 64$

Rearrange:

$2x = 34$

$x = 17$

So the original number $x - 2 = 15.$