document.write( "Question 1121661: In an examination,53% students passed in maths,61% passrd in physics,60% passed in chemistry,24% passed in maths and physics,35% passed in physics and chemistry,27% passed in maths and chemistry and 5% in none. The ratio of percentage of passes in maths and chemistry but not in physics.In relation to percentage of passes in physics and chemistry but not in maths is? \n" ); document.write( "

Algebra.Com's Answer #737666 by ikleyn(52798) $\"\"$ $\"About$

You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "When you solve such problems, the key to success is to introduce compact abbreviations (notations) that work.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let M be the set (and at the same time the percentage) of those who passed Math (53%)\r\n" );
document.write( "\r\n" );
document.write( "    P ------------------------------- \" --------------------------------- Physics (61%)\r\n" );
document.write( "\r\n" );
document.write( "    C ------------------------------- \" --------------------------------- Chemistry (60%)\r\n" );
document.write( "\r\n" );
document.write( "    MP ------------------------------ \" --------------------------------- Math and Physics (24%)\r\n" );
document.write( "\r\n" );
document.write( "    PC ------------------------------ \" --------------------------------- Physics and Chemistry (35%)\r\n" );
document.write( "\r\n" );
document.write( "    MC ------------------------------ \" --------------------------------- Math and Chemistry (27%)\r\n" );
document.write( "   \r\n" );
document.write( "    N ------------------------------- \" --------------------------------- in none\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This \"none\" I interpret in a way that these 5% are not included to either of the categories above and complement the set to 100%.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the only unknown is the intersection MPC of the three sets M, P and C.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is easy to find the measure (the percentage) of MPC.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From the elementary set theory we have this equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    100% = 5% + M + P + C - MP - PC - MC + MPC,    (*)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "which gives you  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    MPC = 100 - 5 - 53 - 61 - 60 + 24 + 36 + 37 = 18%.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now,  in the ratio you want to get, the numerator is  MC - MPC = 27% - 18% = 9%;\r\n" );
document.write( "\r\n" );
document.write( "                                  the denominator is  PC - MPC = 35% - 18% = 17%.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore, the ratio under the question is equal to  . \r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "---------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Regarding the formula (*) see the lesson\r
\n" ); document.write( "\n" ); document.write( " - Advanced problems on counting elements in sub-sets of a given finite set\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );