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**Hint:**We are given that Reena purchased the face cream for ${\text{Rs }}113.40$. Let it include $x\% $ of tax so the rate of tax be $x$ and it is also given that the printed price of the face cream is ${\text{Rs }}105$. So $x\% {\text{ of 105}}$ would be the tax included in the face cream.

**Complete step-by-step answer:**

Here according to the question, Reena purchased the face cream for ${\text{Rs }}113.40$ and also we are given that the actual price of it is${\text{Rs }}105$. So let us assume that the rate of the tax is $x\% $. So the tax is basically to increase the amount of the product by the same amount.

For example: GST which is Goods and Service tax are included, tax includes transportation and other charges.

So here Reena purchased the face cream for ${\text{Rs }}113.40$ but its actual price was ${\text{Rs }}105$ and we assumed the rate of the tax would be $x\% $. So the amount of the tax will be $x\% {\text{ of actual price}}$ that is $x\% {\text{ of 105}}$

Amount of the tax included$ = x\% {\text{ of 105}}$

$ = \dfrac{{x \times 105}}{{100}}$

Now initially its price was ${\text{Rs }}105$ and after the tax it becomes ${\text{Rs }}113.40$

So here total amount is equal to ${\text{Rs }}113.40$ and the total amount is given by the sum of the actual or the printed amount and the amount of the tax included i.e. $\dfrac{{105x}}{{100}}$

So the total amount$ = 105 + \dfrac{{105x}}{{100}}$

So we get the amount$ = 105 + \dfrac{{105x}}{{100}}$

And we know that Reena purchased for ${\text{Rs }}113.40$

So, here the total amount is given that is ${\text{Rs }}113.40$

$\Rightarrow$$113.40 = 105 + \dfrac{{105x}}{{100}}$

$\Rightarrow$$113.40 - 105 = \dfrac{{105x}}{{100}}$

$\Rightarrow$$8.4 = \dfrac{{105x}}{{100}}$

Upon cross multiplication, we get

$\Rightarrow$$8.4(100) = 105x$

$\Rightarrow$$x = \dfrac{{840}}{{105}} = 8$

**So the rate of tax is $8\% $**

**Note:**Here we can do this problem this way also. We know that she purchased for ${\text{Rs }}113.40$ and the actual price was${\text{Rs 105}}$. So the tax included would be equal to $ = 113.40 - 105 = {\text{Rs }}8.4$

So $8.4$ is the amount of tax.

Then what percentage of $105$ is $8.4$

Which is $\dfrac{{105x}}{{100}} = 8.4$

So we get $x = \dfrac{{840}}{{105}} = 8$

So the rate is $8\% $

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