# A shopkeeper offers a 10% off-season discount to the customer and still makes a profit of 26%. What is the cost price of a pair of shoes marked at Rs. 1120?

Answer

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Hint: Calculate the exact amount of discount offered by the shopkeeper first. Then find the selling price and if 26% profit is made on the selling price, find the required cost price.

Complete step-by-step answer:

According to the question, the marked price of the pair of shoes is Rs. 1120. And the shopkeeper is offering a 10% off-season discount. So, discount enjoyed by customer will be:

$ \Rightarrow $ Discount $ = 10\% {\text{ of }}1120 = \dfrac{{10}}{{100}} \times 1120 = 112.$

Thus, the selling price of the shopkeeper will be:

$ \Rightarrow $ S.P. $ = $ Marked Price $ - $ Discount $ = 1120 - 112 = 1008$.

It is given that the shopkeeper makes the profit of 26%. Let the cost price (i.e. C.P.) of the pair of shoes is Rs. $x$. Then profit will be:

$ \Rightarrow $ Profit $ = $ S.P. $ - $ C.P. $ = 1120 - x$

We know that:

$ \Rightarrow {\text{Profit(% )}} = \dfrac{{{\text{Profit}}}}{{{\text{C}}{\text{.P}}{\text{.}}}} \times 100\% $

Using above formula, we have:

$

\Rightarrow 26\% = \dfrac{{1008 - x}}{x} \times 100, \\

\Rightarrow 26x = 100800 - 100x, \\

\Rightarrow 126x = 100800, \\

\Rightarrow x = \dfrac{{100800}}{{126}}, \\

\Rightarrow x = 800 \\

$

Thus the cost price is Rs. 800.

Note: The cost price is always calculated over selling price while the discount is calculated over marked price.

Complete step-by-step answer:

According to the question, the marked price of the pair of shoes is Rs. 1120. And the shopkeeper is offering a 10% off-season discount. So, discount enjoyed by customer will be:

$ \Rightarrow $ Discount $ = 10\% {\text{ of }}1120 = \dfrac{{10}}{{100}} \times 1120 = 112.$

Thus, the selling price of the shopkeeper will be:

$ \Rightarrow $ S.P. $ = $ Marked Price $ - $ Discount $ = 1120 - 112 = 1008$.

It is given that the shopkeeper makes the profit of 26%. Let the cost price (i.e. C.P.) of the pair of shoes is Rs. $x$. Then profit will be:

$ \Rightarrow $ Profit $ = $ S.P. $ - $ C.P. $ = 1120 - x$

We know that:

$ \Rightarrow {\text{Profit(% )}} = \dfrac{{{\text{Profit}}}}{{{\text{C}}{\text{.P}}{\text{.}}}} \times 100\% $

Using above formula, we have:

$

\Rightarrow 26\% = \dfrac{{1008 - x}}{x} \times 100, \\

\Rightarrow 26x = 100800 - 100x, \\

\Rightarrow 126x = 100800, \\

\Rightarrow x = \dfrac{{100800}}{{126}}, \\

\Rightarrow x = 800 \\

$

Thus the cost price is Rs. 800.

Note: The cost price is always calculated over selling price while the discount is calculated over marked price.

Last updated date: 25th Sep 2023

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