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Question
A shopkeeper marks his goods at 40% above the cost price but allows a discount of 5% for cash payment to his customers. What actual profit does he make, if he receives Rs 1064 after paying the discount?
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Solution
\[\text { Let the original cost price of the item be Rs . x } . \]
\[\text { MP = x } + \frac{40x}{100} = 1 . 4x\]
\[\text { Discount = MP - SP }\]
\[MP - \frac{\text { Discount % } \times MP}{100} = SP\]
\[1 . 4x - \frac{5 \times 1 . 4x}{100} = 1064\]
\[\frac{1 . 4x \times 100 - 5 \times 1 . 4x}{100} = 1064\]
\[\text { So, x }\left( 1 . 4 \right)\left( 0 . 95 \right) = 1064\]
\[x = \frac{1064}{\left( 1 . 4 \times 0 . 95 \right)}\]
\[ = \frac{1064}{1 . 33}\]
\[ = Rs . 800\]
\[\text { Profit = Rs } . (1064 - 800)\]
\[ = \text { Rs }. 264\]
\[\text { Thus, the actual profit by the shopkeeper is Rs } . 264 . \]
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