Question

# 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?

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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.

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.