document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=886762>Question 886762</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. When a producer allows 36% commission on the retail price of his product, he earns a profit of 8.8%. What would be his profit percentage if the commission is reduced by 24%?<BR>\n" );
document.write( "2. A and B start a business with invest of tk 5,000 and tk 4,500 respectively. After 4 months, A takes out half of his capital. After 2 more months, B takes out one third of his capital while C joints them with a capital of tk 7,000. At the end of a year, they earn a profit of tk 5,080. Find the share of each member in the profit.<BR>\n" );
document.write( "3. 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #536130 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=536130\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. When a producer allows 36% commission on the retail price of his product, he earns a profit of 8.8%. What would be his profit percentage if the commission is reduced by 24%?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let x = selling price.<BR>\n" );
document.write( "he pays 36% commission so he nets .64*x<BR>\n" );
document.write( "he makes 8.8% profit on that, so his cost has to be .64*x / 1.088 = .5882352941*x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now he reduces his commission by 24%.<BR>\n" );
document.write( "this means the commission is now 12% instead of 36%.<BR>\n" );
document.write( "he now nets .88*x<BR>\n" );
document.write( "since his cost remains the same at .5882352941*x, then his profit becomes .88*x / .5882352941*x = 1.496.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "he will earn 49.6% profit.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let's put this in numbers to see how it pans out.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "he sells the product for $200.00<BR>\n" );
document.write( "he now has to pay out 36% commission on that, so he nets $200.00 minus .36 * $200 which is equal to $128.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "he makes a profit of 8.8% on $128, so his cost had to be $128 / 1.088 = 117.6470588\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now he takes the product that sells for $200 and reduces the commission by 24% which mean the commission is now 12%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "he nets .88 * 200 = 176 dollars.<BR>\n" );
document.write( "his cost remains the same at 117.6470588.<BR>\n" );
document.write( "his new profit is equal to (176 - 117.6470588)/117.6470588 = .496<BR>\n" );
document.write( "he gets 49.6% profits instead of 8.8% by reducing the commission from 36% to 12%.\r<BR>\n" );
document.write( "\n" );
document.write( "-------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2. A and B start a business with invest of tk 5,000 and tk 4,500 respectively. After 4 months, A takes out half of his capital. After 2 more months, B takes out one third of his capital while C joints them with a capital of tk 7,000. At the end of a year, they earn a profit of tk 5,080. Find the share of each member in the profit.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this really depends on what agreement they made up front as to how the money would be split.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a reasonable split would be based on total dollar months invested.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A invests 5000 for 4 months and 2500 for 8 months for a total of 40000.<BR>\n" );
document.write( "B invests 4500 for 6 months and 3000 for 6 months for a total of 45000.<BR>\n" );
document.write( "C invest 7000 for 6 months for a total of 42000.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the total dollar months invested is equal to 127000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A owns 40/127 of that.<BR>\n" );
document.write( "B owns 45/127 of that.<BR>\n" );
document.write( "C owns 42/127 of that.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "they would split the profit by those ratios.<BR>\n" );
document.write( "the profit is 5080.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A gets 40/127 * 5080 = 1600.<BR>\n" );
document.write( "B gets 45/127 * 5080 = 1800.<BR>\n" );
document.write( "C gets 42/127 * 5080 = 1680.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " -------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3. 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "rate * time = quantity of work.l<BR>\n" );
document.write( "let m = rate of the one an<BR>\n" );
document.write( "let b = rate of 1 boy.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get the following equations:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(2m + 3b) * 10 = 1<BR>\n" );
document.write( "(3m + 2b) * 8 = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify these to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "20m + 30b = 1<BR>\n" );
document.write( "24m + 16b = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve these equations simultaneously to get b = 1/100 and m = 7/200.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "those are your solutions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "plug those solutions back into the original equations and you will see that they are confirmed as correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(2 * 7/200 + 3 * 1/100) * 10 = 1<BR>\n" );
document.write( "(3 * 7/200 + 2 * 1/100) * 8 = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can now use these rates to solve the problem.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(2m + 1b) * x = 1 becomes:<BR>\n" );
document.write( "2 * 7/200 + 1 * 1/100) * x = 1<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "(14/200 + 1/100) * x = 1<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "16/200 * x = 1<BR>\n" );
document.write( "divide both sides of this equation by 16/200 to get:<BR>\n" );
document.write( "x = 1 * 200/16 = 12.5 days.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );