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CBSE Class 9 Answered

Students in a school are made to stand in a row and column formation. In an average day, the number of rows and the number of columns is fixed. On one particular day, the row size was increased by 4, which lead to the number of rows decreasing by 2. On another day, the row size was decreased by 4, which led to the no. of rows increasing by 4. How many students are there in the school?
Asked by a.behera67 | 25 Jan, 2016, 08:07: PM
answered-by-expert Expert Answer
Let space straight m space be space the space number space of space rows space and space straight n space be space the space number space of space colums space and space straight k space be space the space total space number space of space students. therefore mn space equals space straight k.......... left parenthesis 1 right parenthesis On space one space particular space day comma space the space row space size space was space increased space by space 4 comma space which space lead space to space the space number space of space rows space decreasing space by space 2. therefore left parenthesis straight m plus 4 right parenthesis left parenthesis straight n minus 2 right parenthesis space equals space straight k mn minus 2 straight m plus 4 straight n minus 8 equals straight k straight k space minus 2 straight m space plus 4 straight n space minus 8 space equals straight k....... left square bracket from space left parenthesis 1 right parenthesis right square bracket space minus 2 straight m space plus 4 straight n space space equals 8........ left parenthesis 3 right parenthesis On space another space day comma space the space row space size space was space decreased space by space 4 comma space which space led space to space the space no. space of space rows space increasing space by space 4 therefore left parenthesis straight m minus 4 right parenthesis left parenthesis straight n plus 4 right parenthesis space equals space straight k mn plus 4 straight m minus 4 straight n minus 16 equals straight k straight k space plus 4 straight m space minus 4 straight n space minus 16 space equals straight k....... left square bracket from space left parenthesis 1 right parenthesis right square bracket space 4 straight m space minus 4 straight n space space equals 16........ left parenthesis 4 right parenthesis Adding space eq space left parenthesis 3 right parenthesis space and space left parenthesis 4 right parenthesis space we space get comma 2 straight m space equals 24 straight m space equals 12 Substitute space straight m space equals 12 space in space eq space left parenthesis 3 right parenthesis space we space get minus 24 plus 4 straight n space equals 8 4 straight n space equals space 32 straight n space equals 8 Total space number space of space students space equals 12 cross times 8 space equals 96
Answered by Vijaykumar Wani | 27 Jan, 2016, 11:25: AM

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