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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. Q.4

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What is the best solution for this optional exercise of class 10th 3.7. How i solve easily this question 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.

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  1. Let the number of rows be A and the number of students in a row be B.

    Total number of students = Number of rows x Number of students in a row

    =AB

    Using the information, that is given,

    First Condition:

    Total number of students = (A – 1) ( B + 3)

    Or AB = ( A – 1 )(B + 3) = AB – B + 3A – 3

    Or 3A – B – 3 = 0

    Or 3A – Y = 3 – – – – – – – – – – – – – (1)

    Second condition:

    Total Number of students = (A + 2 ) ( B – 3 )

    Or AB = AB + 2B – 3A – 6

    Or 3A – 2B = -6 – – – – – – – – – (2)

    When equation (2) is subtracted from (1)

    (3A – B) – (3A – 2B) = 3 – (-6)

    -B + 2B = 3 + 6B = 9

    By using the equation (1) we get,

    3A – 9 =3

    3A = 9+3 = 12

    A = 4

    Number of rows, A = 4

    Number of students in a row, B = 9

    Number of total students in a class = AB = 4 x 9 = 36

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