document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=887033>Question 887033</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man fixed the selling price of his goods at a profit of 10%. while selling his goods he by mistake gave some commission and there was a loss of 1%. what percent was the commission.  </SPAN>\n" );
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document.write( "to make a 10% profit, the selling price has to be 1.10 * the cost.\r<BR>\n" );
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document.write( "to make a loss of 1%, the selling price has to be .99 * the cost.\r<BR>\n" );
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document.write( "the difference in the selling price is 1.10 * the cost  - .99 * the cost = .11 * the cost.\r<BR>\n" );
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document.write( ".11 * the cost divided by 1.10 * the cost = .11 / 1.10 = .10 which is equal to 10%.\r<BR>\n" );
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document.write( "the commission had to be 10%.\r<BR>\n" );
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document.write( "let's put this in numbers so you can see how it works.\r<BR>\n" );
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document.write( "the cost is 100 dollars.\r<BR>\n" );
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document.write( "to make 10% profit, the selling price is 110 dollars.\r<BR>\n" );
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document.write( "if he sells at 110 dollars and gets to keep it all, then the profit is 110 - 100 = 10 dollars which is equal to 10% of the cost of 100 dollars.\r<BR>\n" );
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document.write( "but, he gives out a 10% commission by mistake.\r<BR>\n" );
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document.write( "10% of 110 dollars is equal to 11 dollars.\r<BR>\n" );
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document.write( "instead of netting 110 dollars, he now nets 99 dollars because he gave out a commission of 11 dollars on the sale by mistake.\r<BR>\n" );
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document.write( "the profit is 99 dollars - 100 dollars equals -1 dollars.<BR>\n" );
document.write( "-1 dollars divided by 100 dollars is equal to a profit of -.01 which is equal to a profit of -1% of the cost.\r<BR>\n" );
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document.write( "a profit of -1% of the cost is the same as a loss of 1% of the cost because negative profit is equal to loss.\r<BR>\n" );
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document.write( "the solution to the problem is that the commission was 10% of the selling price.\r<BR>\n" );
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