document.write( "Question 990633: Rahul average goes by 1 after scoring 21. His average goes by 2 more after the next score of 35. what is the total runs scored by rahul including 21 and 35 ? \n" ); document.write( "

Algebra.Com's Answer #610646 by anand429(138) $\"\"$ $\"About$

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Let total runs scored before = x
\n" ); document.write( "No of innings = y
\n" ); document.write( "Avg. = x/y
\n" ); document.write( "After scoring 21,
\n" ); document.write( "Avg. = (x+21)/(y+1) which should be equal to (x/y) + 1
\n" ); document.write( "or, $\"%28x%2B21%29%2F%28y%2B1%29+=+%28x%2Fy%29+%2B+1+\"$
\n" ); document.write( "=> $\"y%28x%2B21%29+=+%28y%2B1%29%2A%28x%2By%29\"$
\n" ); document.write( "=> $\"xy+%2B+21y+=+xy+%2B+y%5E2+%2B+x+%2B+y\"$
\n" ); document.write( "=> $\"y%5E2+-+20y+%2B+x+=+0+\"$ ------------------------(i)
\n" ); document.write( "Similarly,
\n" ); document.write( " $\"%28x%2B21%2B35%29%2F%28y%2B2%29+=+%28x%2Fy%29+%2B+3\"$
\n" ); document.write( "=> $\"yx+%2B+56y+=+xy+%2B+2x+%2B+3y%5E2+%2B+6y\"$
\n" ); document.write( "=> $\"3y%5E2+-+50y+%2B+2x+=+0\"$ -----------------------(ii)
\n" ); document.write( "Multiplying (i) by 2, we get,
\n" ); document.write( " $\"2y%5E2+-+40y+%2B+2x+=+0+\"$ ------------------------(iii)
\n" ); document.write( "Subtracting (iii) from (ii)
\n" ); document.write( " $\"y%5E2+-10y+=+0\"$
\n" ); document.write( "=> y = 10 (Since y can not be 0)
\n" ); document.write( "Putting in (i)
\n" ); document.write( "100-200 + x = 0
\n" ); document.write( "=> x = 100
\n" ); document.write( "So runs scored including 21 and 35 = 100 +21 +35 = 156 \n" ); document.write( "

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