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Question

A dealer sells a table at $$20\%$$ profit. Had he purchased it for $$6\%$$ lesser cost and sold for Rs. $$50$$ less he would have earned a profit of $$25\%$$. Find the cost of the table.


Solution

Let the cost of table $$= Rs. x$$
Profit $$= 20\%$$
$$SP = Cost + Profit = x + 20\%$$ of $$x$$ $$=x + \cfrac{x}{5} = \cfrac{6x}{5}$$
Now, New cost price $$=x - \cfrac{6}{100}\times x$$ $$=\cfrac{94x}{100}$$
New selling price $$=\cfrac{6x}{5} - 50$$
New Profit = New SP - New CP $$=\cfrac{6x}{5} - 50 - \cfrac{94x}{100} = \cfrac{26x}{100} - 50$$
New Profit $$= 25\%$$ of New CP $$=\cfrac{25}{100}\times \cfrac{94x}{100} = \cfrac{47x}{200}$$
Hence, $$\cfrac{47x}{200} = \cfrac{26x}{100} - 50$$
$$\cfrac{47x - 52x}{200} = -50$$
$$5x = 200 \times 50$$
$$x = 2000 Rs$$
Thus, Cost Price $$= Rs. 2000$$

Mathematics

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