Question

The average price of 12 SKUs increases by Rs 10 when a new SKU is replaced with an SKU, price of which was Rs 105. What would be the price of the new SKU

Answer 1

Formula for average:

$Average = \dfrac{\text {Total sum of observations}}{\text{Total number of observations}}$

Let original average be $x$ and original total price be $y$. Here, total number of units are 12.

So, according to the formula:

$x = \dfrac{y}{12} ...... (1)$

Now, an old SKU (with price 105 Rs.) has been replaced with a new priced SKU and new average is increased by 10 (i.e. $x + 10$).

Let total price becomes $y'$. According to the formula, new equation becomes:

$x + 10 = \dfrac{y'}{12}$

Putting the value of $x$ from equation (1):

$\Rightarrow \dfrac{y}{12} + 10 = \dfrac{y'}{12}\\\Rightarrow y' = y + 120$

It means that new total price of SKUs has increased by 120 due to replacement of one SKU. It means that its price is 120 more than the previous SKU.

The price of previous SKU was Rs. 105, so price of new SKU = 105 + 120

So, the price of new SKU is Rs. 225.