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Students ofa class are preparing for a drill and are made to stand in rows. If 4students are extra in a row, then there would be 2 rows less. But there wouldbe 4 more rows if 4 students are less in a row. The number of students in theclass is(a) 56 (b) 65 (c) 69 (d) 96 |
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Answer» Let the number of rows be x and the number of students in each row be y. Then, the total number of students = xy . Case I When there are 4 more students in each row = ( y + 4) And, number of rows = (x - 2 ) Total number of students = (x - 2) ( y + 4) `therefore (x - 2) ( y + 4) = xy rArr 4x - 2y = 8 ` `" " rArr 2 x - y = 4 " " `... (i) Case II When 4 students are removed from each row. Then, number of students in each row = ( y - 4) And, number of rows = ( x+ 4) Total number of stuents = ( x+ 4 ) ( y - 4) ` therefore (x + 4 ) ( y - 4) = xy rArr 4 y - 4x = 16` `" " rArr 4 ( y - x) = 16 ` ` " " rArr ( y - x ) = 4 " " `... (ii) Adding (i) and (ii), we get x = 8 Putting ` x = 8` in (ii), we get ` y- 8 = 4 rArr y = 12 ` Thus, x = 8 and y = 12 This shows that there are 8 rows and there are 12 students in each row. Hence, the number of students in the class = ` xy = 8 xx 12 = 96`. |
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