document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1072148>Question 1072148</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Samay has some sugar worth Rs 3000. He sold one-third at a loss of 10%.By how much percentage must the selling price be increased in the remaining so that there is a gain of 10% in outlay after allowing 20% discount . </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #687043 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=687043\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> two ways to look at this because i'm not understanding exactly what you're looking for.\r<BR>\n" );
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document.write( "does he want to make 10% gain on the remaining 2/3, or does he want to make 10% gain on the whole thing?\r<BR>\n" );
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document.write( "i'm assume he wants to make 10% gain on the whole thing, including the part where he took a 10% loss.\r<BR>\n" );
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document.write( "if that's not what you want, then let me know and i'll re-work the solution accordingly.\r<BR>\n" );
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document.write( "he has merchandise that cost him 3000.\r<BR>\n" );
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document.write( "he sells 1/3 of this at a loss of 10%.\r<BR>\n" );
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document.write( "1/3 * 3000 = 1000 from which he received revenue of 900 which gave him the 10% loss of 100.\r<BR>\n" );
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document.write( "he has 2/3 of the 3000 left which means he has 2000 worth of merchandise left to sell.\r<BR>\n" );
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document.write( "he wants to make an overall gain of 10% on the 3000 worth of merchandise.\r<BR>\n" );
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document.write( "10% of 3000 is equal to 300.\r<BR>\n" );
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document.write( "the total gain he wants to make is 300 from the remaining 2000.\r<BR>\n" );
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document.write( "he wants to sell the remaining 2000 at a 20% discount from the retail price.\r<BR>\n" );
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document.write( "what he is saying is that the selling price has to be 80% of the retail price.\r<BR>\n" );
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document.write( "to make a profit of 300, then the selling price minus the cost of 2000 must be equal to 300.\r<BR>\n" );
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document.write( "let R equal the retail price and let S = the selling price and let C = the cost and let P equal the profit.\r<BR>\n" );
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document.write( "the equation would start out as S - C = P\r<BR>\n" );
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document.write( "this means selling price minus cost = profit.\r<BR>\n" );
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document.write( "since S = .80 * R, the equation becomes .80 * R - C = P\r<BR>\n" );
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document.write( "this means 80% of the retail price minus the cost is equal to profit.\r<BR>\n" );
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document.write( "since P = 300 and C = 2000, the equation becomes .80 * R - 2000 = 300\r<BR>\n" );
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document.write( "add 300 to both sides of this equation to get .80 * R = 2300.\r<BR>\n" );
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document.write( "divide both sides of this equation by .80 to get R = 2300 /.8 = 2875.\r<BR>\n" );
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document.write( "the retail price has to be 2875.\r<BR>\n" );
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document.write( "discount is 20% of 2875 = 575.<BR>\n" );
document.write( "2875 - 575 = 2300.\r<BR>\n" );
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document.write( "selling price is equal to 2300.\r<BR>\n" );
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document.write( "cost of the remaining merchandise is 2000 which makes the profit = 300.\r<BR>\n" );
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document.write( "original cost is 3000.\r<BR>\n" );
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document.write( "profit is 300.\r<BR>\n" );
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document.write( "percent profit is 300 / 3000 * 100 = 10%.\r<BR>\n" );
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document.write( "by charging a retail price of 2875 for the remaining 2000 worth of merchandise, he can give a 20% discount to make the selling price 2300 which gives him 300 profit which is 10% of the overall cost of 3000 worth of merchandise.\r<BR>\n" );
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document.write( "at least, i think this is what you're asking.\r<BR>\n" );
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document.write( "if different, let me know what's different and i'll rework it for you based on that new understanding.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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