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A shopkeeper marks his goods at such a price that would give him a profit of $10\% $ after allowing a discount of $12\% $ .If an article is marked at $Rs2250$. Find its cost price.
(A) $1800$
(B) $1600$
(C) $1700$
(D) $1750$

Answer Verified Verified
Hint: Try to imagine the whole situation from the perspective of the shopkeeper. Take the marked price and go step by step with the discount and then the profit. Find the selling price, which will help you in finding the cost price using profit.

Complete step-by-step answer:
Given data in the question is that the marked price on the product (MP) is $Rs2250$, discount offered is of $12\% $ of the marked price and the shopkeeper still makes a profit of $10\% $.
Here, for finding the price at which the shopkeeper is selling the goods, i.e. selling price (SP) you need to take away the discount from marked price.
Selling price $ = $ Marked Price $ - $ Discount offered
Now let’s put the known values in this relation
$SP = MP - 12\% of MP \Rightarrow SP = 2250 - \dfrac{{12}}{{100}} \times 2250$
Therefore, $SP = 2250 - 270 = Rs.1980$
We got the selling price at which the shopkeeper is selling the goods. According to the question, at this selling price, he is still making a profit of $10\% $, i.e. the selling price of the good must be $10\% $ more of the cost price of the good.
$ \Rightarrow SP = CP + 10\% of CP \Rightarrow SP = CP\left( {1 + \dfrac{{10}}{{100}}} \right) \Rightarrow SP = CP\left( {\dfrac{{110}}{{100}}} \right)$
Let’s use our known value of SP in the above relation
$1980 = CP \times \dfrac{{11}}{{10}} \Rightarrow CP = \dfrac{{1980 \times 10}}{{11}} \Rightarrow CP = Rs.1800$
Hence, the cost price of the goods is $Rs.1800$.

Note: Try to understand the question well by reframing it in your own words. Go step by step to make the process less complicated. An alternative approach for the above problem can be the use the formula for profit, i.e. Profit$\% = \left( {\dfrac{{SP - CP}}{{CP}}} \right) \times 100$. This formula could be used after finding out the selling price.