Question

A shopkeeper sells an article for ${\text{Rs }}21,384$ including $10\% $ tax. However, the actual rate of tax is $8\% $. Find the extra profit made by the dealer.

Answer 1

Hint: In this question, the concept of the selling price and the tax will be used that is initially calculate the actual price of the article that a shopkeeper sells by using the given formula then add the actual rate of tax in this value, so we can get the extra profit that is made by the dealer.

Formula used:
The actual price of an article is calculated as,
${\text{AP}} = {\text{SP}} \times \left( {\dfrac{{100}}{{100 + {\text{rate}}}}} \right)$
Where, AP is the actual price, SP is the selling price, and rate is the tax.

Complete step by step solution:
We know that the price at which an item is purchased is its cost price and the price at which an item is to be sold is its selling price. When selling price is greater than cost price, we have profit and when selling price is less than cost price, we have loss.
Every product has a cost price ${\text{CP}}$ and selling price ${\text{SP}}$.
Profit and loss formula are used to find the price of any item in the market
The ${\text{SP}}$of an article is $21,384$ and it includes tax@$10\% $.
The actual price of an article is calculated as,
${\text{AP}} = {\text{SP}} \times \left( {\dfrac{{100}}{{100 + {\text{rate}}}}} \right)$
Now, we substitute the given value in the above equation as,
${\text{AP}} = 21,384 \times \left( {\dfrac{{100}}{{100 + 10}}} \right)$
$ \Rightarrow {\text{AP}} = {\text{Rs}}\;19,440$
But the actual rate of tax is $8\% $. so, calculate the sale price of the article for the same.
The sale price at $8\% $ is calculated as,
\[{\text{SP}} = {\text{AP}} + {\text{Tax}}\]
Now, we substitute the given value in the above equation as,
\[{\text{SP}} = 19,440 + 1555.2\]
\[ \Rightarrow {\text{SP}} = {\text{Rs}}\;20,995.2\]
Now, we calculate the extra profit as,
${\text{Profit}} = {\text{SP at 10% }} - {\text{SP at 8% }}$
Now, we substitute the given value in the above equation as,
${\text{Profit}} = 21,384 - 20,995.2$
$\therefore {\text{Profit}} = {\text{Rs}}\;388.8$

Therefore, the extra profit made by the dealer is ${\text{Rs}}\;388.8$ at tax $8\% $.

Note: In this question, calculate the actual price of the article instead of deducting $2\% $from the amount $21,384$ Make sure that always calculate the actual price otherwise the Answer must be wrong. Do the calculation carefully and avoid silly mistakes.