document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1002078>Question 1002078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Price of sugar is increased by 20% if the expenditure on sugar has to be kept the same as earlier the ratio between the reduction in consumption and the original consumption is?? (In short method) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #619086 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=619086\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the original consumption.<BR>\n" );
document.write( "let y = the original price.<BR>\n" );
document.write( "the expenditure is therefore equal to x*Y.\r<BR>\n" );
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document.write( "if you raise the new price by 20%, then the new price is equal to 1.2 * y\r<BR>\n" );
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document.write( "1.2 * y is the same as 6/5 * y\r<BR>\n" );
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document.write( "in order to keep the expenditure the same, the original consumption needs to be divided by 1.2.\r<BR>\n" );
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document.write( "divided by 1.2 is the same as multiplying by 1/1.2\r<BR>\n" );
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document.write( "multiplying by 1/1.2 is the same as multiplying by 5/6.\r<BR>\n" );
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document.write( "if the original price is multiplied by 6/5, the original consumption has to be multiplied by 5/6 in order to keep the total expenditure the same.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "expenditure = x * y\r<BR>\n" );
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document.write( "expenditure = 5/6 * x * 6/5 * y = x * y\r<BR>\n" );
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document.write( "the expenditure remains the same.\r<BR>\n" );
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document.write( "the problem is stated as shown below:\r<BR>\n" );
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document.write( "Price of sugar is increased by 20% if the expenditure on sugar has to be kept the same as earlier the ratio between the reduction in consumption and the original consumption is?\r<BR>\n" );
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document.write( "they are looking for the ratio between the reduction in consumption and the original consumption.\r<BR>\n" );
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document.write( "if the original consumption is x and the reduced consumption is 5/6 * x, then the reduction in consumption is 1/6 * x.\r<BR>\n" );
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document.write( "the ratio between the reduction in consumption and the original consumption is therefore 1/6 * x / x which results in 1/6.\r<BR>\n" );
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