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Kunal bought a suitcase with $15%$ discount on the labeled price. He sold the suitcase for Rs. \[2880\] with $20%$ profit on the labeled price. At what price did he buy the suitcase?
(a) $Rs.2040$
(b) $Rs.2400$
(c) $Rs.2604$
(d) $Rs.2640$

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Last updated date: 21st Feb 2024
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IVSAT 2024
Answer
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Hint: In the above question, we have given the selling price and profit and discount on the labeled price of the suitcase. Now, we have to find the price with which he buys the suitcase which is indirectly the cost price of the suitcase. Now, to find the cost price of the suitcase, we have to firstly calculate the labeled price. Now, after calculating the labeled price, we will use the discount given on the labeled price to find the cost price of the suitcase.

Complete step by step solution:
In the above question, we are given that
The selling price of the suitcase $=2880$
Profit Kunal gets after selling the suitcase on labeled price is $20%$
Let the labeled price of the suitcase be $x$.
Now, we know that Selling price is $120%$ of the labeled price, as Kunal gets $20%$ profit selling the suitcase on the labeled price.
So, we write that $120%$ of $x$ is $2880$
We get,
$\Rightarrow 120%\left( x \right)=2880$
$\Rightarrow \dfrac{120}{100}x=2880$
$\Rightarrow x=2880\times \dfrac{100}{120}$
$\Rightarrow x=2400$
Hence, the labeled price is \[2400\].
Now, we know that Kunal bought the suitcase with the $15%$ on the labeled price.
So, we can write that the Cost price is $85%$ of the labeled price.
So, C.P. is $85%$ of Rs. \[2400\],
We get,
$\Rightarrow 85%\left( 2400 \right)$
$\Rightarrow \dfrac{85}{100}\left( 2400 \right)$
$\Rightarrow 2040$
Hence, the cost price of the suitcase is Rs. \[2040\]

Hence, the correct option is \[a\].

Note: In this type of problem we have to remember some important points that whenever the percentage of the profit and the percentage of the loss id equal the \[%\] loss is equal to the square of the power which is divided by \[100\].
\[\text{ }\!\!%\!\!\text{ loss = }\dfrac{{{\text{P}}^{\text{2}}}}{\text{100}}\]
Also when the profit will be \[m%\] and loss will be \[n%\] then the net percentage for profit and loss will be:
\[\dfrac{(m-n-mn)}{100}\]