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Last updated at May 29, 2018 by Teachoo

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Ex 3.7, 4 (Introduction) The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class. Introduction Let 2 Students stand in 1 row and there are 10 rows in total Total the number of Students = Number of Students in 1 row Number of rows = 2 10 = 20 Students We will use the formula Total number of Students = Number of Students in 1 row Number of rows Ex 3.7, 4 The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class. Let number of students in 1 row = x and number of rows = y Then, Total number of Students = Number of Students in 1 row Number of rows Total number of Students = xy If 3 Students are extra in a row, there would be 1 row less. Hence, If 3 Students are less in a row, there would be 2 row less. Hence, Number of students in 1 row = x + 3 Number of rows = y 1 Now, Total Number of Students = Number of Students in 1 row Number of rows = (x + 3) (y 1) Putting number of Students = xy xy = (x + 3) (y 1) (x + 3) (y 1) = xy x (y 1) + 3 (y 1) = xy xy x + 3y 3 = xy xy x + 3y 3 = 0 x 3y + 3 = 0 Number of Students in 1 row = x 3 Number of rows = y + 2 Now, Total Number of Students = Number of Students in 1 row Number of rows = (x 3) (y + 2) Putting number of Students = xy xy = (x 3) (y + 2) (x 3) (y + 2) = xy x (y + 2) 3 (y + 2) = xy xy + 2x 3y 6 = xy 2x 3y 6 = xy xy 2x 3y 6 = 0 Hence, equations are x 3y + 3 = 0 (2) 2x 3y 6 = 0 (3) From equation (2) x 3y + 3 = 0 x = 3y 3 Putting x = 3y 3 in equation (3) 2x 3y 6 = 0 2 (3y 3) 3y 6 = 0 6y 6 3y 6 = 0 3y 12 = 0 3y = 12 y = 12/3 y = 4 Putting y = 4 in equation (2) x 3y + 3 = 0 x (3 4) + 3 = 0 x 12 + 3 = 0 x 9 = 0 x = 9 Therefore, Number of Students in 1 row = x = 9 Number of rows = y = 4 Total Number of Students = Number of Students in 1 row Number of rows = 9 4 = 36

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.