Question

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

Answer 1

Hint: Whenever we have this type of problem, first find the actual price considering $8\% $ tax, then subtract both the prices that are calculated from the given price to find the extra profit made by the dealer. In order to find the actual price make use of the formula given by: $AP = SP \times \left( {\dfrac{{100}}{{100 + rate}}} \right)$.

Complete step by step answer:
Here in this type of problems, first analyze the question of what they gave. They have given a selling price as \[Rs.21,384\] including $10\% $ tax. And also they have given the actual tax as $8\% $.
Now to find the extra profit made by the dealer first we need to find the actual price considering $10\% $ tax and then find the actual price for $8\% $ tax.
In order to find the actual price make use of the formula given by:
$AP = SP \times \left( {\dfrac{{100}}{{100 + rate}}} \right)$
Where, $AP$ is actual price
              $SP$ is the selling price of an article which is \[Rs.21,384\]
             Rate is the tax in this problem.
First we need to find the actual price for $10\% $ tax.
Therefore, we get
$AP = 21,384 \times \left( {\dfrac{{100}}{{100 + 10}}} \right)$
On simplifying the above expression, we get
$ \Rightarrow AP = 21,384 \times \left( {\dfrac{{100}}{{110}}} \right)$
$ \Rightarrow AP = 19,440$
The actual price considering $10\% $ tax is calculated because if we add $8\% $ tax of the actual price to the actual price we get the selling price of $8\% $ tax.
Now, we need to find the selling price at $8\% $ tax.
$19,440 = SP \times \left( {\dfrac{{100}}{{100 + 8}}} \right)$
On simplifying the above expression, we get
$19,440 \times \left( {\dfrac{{100 + 8}}{{100}}} \right) = SP$
$ \Rightarrow SP = 19,440 \times \left( {\dfrac{{108}}{{100}}} \right)$
$ \Rightarrow SP = 19,440 \times 1.08$
$ \Rightarrow SP = 20,995.2Rs$
Now, in order to find the extra profit we can write as below.
Extra profit $ = $ selling price including $10\% $ tax $ - $ selling price for $8\% $ tax.
Extra profit $ = 21,384 - 20995.2$

Therefore, Extra profit $ = 388.8Rs$

Note:
Whenever we have this type of problem, first we need to know how to find the actual price, which is necessary to calculate the selling price for considering $8\% $ tax. As they have asked for extra profit without the calculation of actual price of an article you may get the wrong answer. Be careful while solving the problems.