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Reena purchased a face cream for ${\text{Rs }}113.40$ including the tax. If the printed price of the face cream is ${\text{Rs }}105$, find the rate of the tax on it.

Last updated date: 19th Sep 2024
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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.

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 $8\%$