document.write( "Question 1194891: In MBA 45th batch, 40% of the girls are fair and the reminder is brown. Half of the girl are beautiful and half are moderate. If 10% of the girls are fair and beautiful, and 40 girls are brown and moderates, how many girls are fair and moderate? \n" ); document.write( "

Algebra.Com's Answer #827206 by ikleyn(53763) $\"\"$ $\"About$

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\n" ); document.write( "In MBA 45th batch, 40% of the girls are fair and the $\"highlight%28cross%28reminder%29%29\"$ remainder is brown.
\n" ); document.write( "Half of the girl are beautiful and half are moderate.
\n" ); document.write( "If 10% of the girls are fair and beautiful, and 40 girls are brown and moderates,
\n" ); document.write( "how many girls are fair and moderate?
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document.write( "In the set of all girls in MBA 45th batch, we have 4 subsets:\r\n" );
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document.write( "    - F (fair, 40%);\r\n" );
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document.write( "    - R (brown, 60%);\r\n" );
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document.write( "    - B (beautiful, 50%);\r\n" );
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document.write( "    - M (moderate, 50%).\r\n" );
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document.write( "We also are given in-pair intersections\r\n" );
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document.write( "    - FB (fair and beautiful, 10%);\r\n" );
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document.write( "    - RM (brown and moderate, 40 girls).\r\n" );
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document.write( "From it, the union \r\n" );
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document.write( "    F U B = 40% + 50% - 10% = 80%  (fair or beautiful).\r\n" );
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document.write( "The complement for (F U B) is the set RM = (R and M) = (brown and moderate); so it contains 100%-80% = 20%.\r\n" );
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document.write( "From the other side, the set (brown and moderate) is 40 girls;\r\n" );
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document.write( "So, the total girls in MBA 45th batch is  40/0.2 = 200.\r\n" );
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document.write( "    +-----------------------------------------------+\r\n" );
document.write( "    |    OK.  Half of the problem is just solved.   |\r\n" );
document.write( "    |          Now let' solve the rest.             |\r\n" );
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document.write( "Notice, that the sought set FM = (fair and moderate)  is the complement \r\n" );
document.write( "of the set FB (fair and beautiful) to F (fair).\r\n" );
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document.write( "In other words,  FM = F \ FB.\r\n" );
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document.write( "Hence,  FM is 40% minus 10% :  FM = 40% - 10% = 30%.\r\n" );
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document.write( "30% of 200 is 0.3*200 = 60.\r\n" );
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document.write( "ANSWER.  In MBA 45th batch, there are 60 girls fair and moderate.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Really good entertainment problem.\r
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