The mean of 40 items is 35 and if each item is multiplied by 'a' then the mean will be :

We are given that the mean of 40 items is 35. First off, the mean of any set of numbers is calculated by dividing the sum of the numbers by the number of items. In this case, the formula for the mean is:

Mean = Sum of items / Number of items

So, from the problem, we know that the mean of the 40 items is 35, which can be written mathematically as:

Sum of items / 40 = 35

By multiplying both sides by 40, we can find the sum of the items:

Sum of items = 35 × 40 = 1400

Now, the next part of the question asks what happens if each of these 40 items is multiplied by a constant 'a'. This means that each individual value in the set is now 'a' times the original value.

Let's think about how the new sum is affected. If each original item is multiplied by 'a', then the new sum of the items will be:

New sum of items = a × (Sum of original items) = a × 1400 = 1400a

So, the new sum is now 1400a. Now, to find the new mean, we take this new sum and divide it by the same number of items, which is still 40. This gives us the new mean:

New mean = New sum of items / 40 = 1400a / 40

Simplifying this:

New mean = 35a

So, the correct answer is 35a. This shows that if each item is multiplied by 'a', the mean will also be multiplied by 'a'. The mean is no longer a fixed value of 35 it scales with the constant 'a'. This tells us that the mean changes proportionally with the multiplication factor.