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Question
A shopkeeper allows 20% off on the marked price of goods and still gets a profit of 25%. What is the actual cost to him of an article marked Rs 500?
Solution
\[\text { Given }, \]
\[\text { MP of an article = Rs } . 500\]
\[\text { Discount = 20 % } \]
\[\text { Therefore, Discount = 20 % of } 500\]
\[ = 0 . 20 \times 500\]
\[ = 100\]
\[\text { So, SP = MP - Discount }\]
\[ =\text { Rs } . (500 - 100)\]
\[ = \text { Rs } . 400\]
\[\text { CP } = \left[ \frac{100}{\left( 100 +\text { Gain % } \right)} \times\text { SP } \right]\]
\[ = \left[ \frac{100}{\left( 100 + 25 \right)} \times 400 \right]\]
\[ = \frac{40000}{125}\]
\[ = Rs . 320\]
\[\text { Thus, the actual cost of the article is Rs } . 320 .\]
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