document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175135>Question 175135</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In an examination, 75% students passed in science, 65% passed in mathematics and 15% failed in both the subjects. If the total number of students who passed in both the subjects was 475, find the total number of students who appeared in the examination </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130280 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=130280\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A++circle%28+-3%2C+0%2C+4+%29%2C%0D%0A++circle%28+2%2C+0%2C+6+%29%2C%0D%0A++rectangle%28+-7%2C+-8%2C+8%2C+8+%29%2C%0D%0A++locate%28+-5%2C+0%2C+M%5Bp%5D+%29%2C+locate%28+4%2C+0%2C+S%5Bp%5D+%29%2C+locate%28+-2%2C+0%2C+SM%5Bp%5D+%29%2C+%0D%0Alocate%28+-5%2C+7%2C+SM%5Bf%5D+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In the above figure, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bp%5D ALIGN=MIDDLE  ALT=\"S%5Bp%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents the set of all students who passed in only Science, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5Bp%5D ALIGN=MIDDLE  ALT=\"M%5Bp%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents the set of all students who passed in only Mathematics, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SM%5Bp%5D ALIGN=MIDDLE  ALT=\"SM%5Bp%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents the set of all students who passed in both Science and Mathematics and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SM%5Bf%5D ALIGN=MIDDLE  ALT=\"SM%5Bf%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents the set of all students who failed in both Science and Mathematics.\r<BR>\n" );
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document.write( "Let the total no. of students = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N ALIGN=MIDDLE  ALT=\"N\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So we can write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bp%5D+%2B+M%5Bp%5D+%2B+SM%5Bp%5D+%2B+SM%5Bf%5D+=+N+ ALIGN=MIDDLE  ALT=\"S%5Bp%5D+%2B+M%5Bp%5D+%2B+SM%5Bp%5D+%2B+SM%5Bf%5D+=+N+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ______ (1)\r<BR>\n" );
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document.write( "It is given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SM%5Bp%5D+=+475 ALIGN=MIDDLE  ALT=\"SM%5Bp%5D+=+475\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Again, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bp%5D+%2B+SM%5Bp%5D+=+0.75N ALIGN=MIDDLE  ALT=\"S%5Bp%5D+%2B+SM%5Bp%5D+=+0.75N\"   DISABLED_style= \"max-width:90%; height:auto;\" > i.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bp%5D+%2B+475+=+0.75N ALIGN=MIDDLE  ALT=\"S%5Bp%5D+%2B+475+=+0.75N\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Also, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5Bp%5D+%2B+SM%5Bp%5D+=+0.65N ALIGN=MIDDLE  ALT=\"M%5Bp%5D+%2B+SM%5Bp%5D+=+0.65N\"   DISABLED_style= \"max-width:90%; height:auto;\" > i.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5Bp%5D+%2B+475+=+0.65N ALIGN=MIDDLE  ALT=\"M%5Bp%5D+%2B+475+=+0.65N\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Further, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SM%5Bf%5D+=+0.15N ALIGN=MIDDLE  ALT=\"SM%5Bf%5D+=+0.15N\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Substituting these into equation (1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.75N+-+475+%2B+0.65N+-+475+%2B+475+%2B+0.15N+=+N+ ALIGN=MIDDLE  ALT=\"0.75N+-+475+%2B+0.65N+-+475+%2B+475+%2B+0.15N+=+N+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.55N+-+475+=+N+ ALIGN=MIDDLE  ALT=\"1.55N+-+475+=+N+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.55N+-+N+=+475+ ALIGN=MIDDLE  ALT=\"1.55N+-+N+=+475+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.55N+=+475+ ALIGN=MIDDLE  ALT=\"0.55N+=+475+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+=+475%2F0.55+ ALIGN=MIDDLE  ALT=\"N+=+475%2F0.55+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+=+95 ALIGN=MIDDLE  ALT=\"N+=+95\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Thus, a total of 95 students appeared for the examination. </SPAN>\n" );
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