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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 â€“ 1) ( B + 3)

Or AB = ( A â€“ 1 )(B + 3) = AB â€“ B + 3A â€“ 3

Or 3A â€“ B â€“ 3 = 0

Or 3A â€“ Y = 3 â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ (1)

Second condition:

Total Number of students = (A + 2 ) ( B â€“ 3 )

Or AB = AB + 2B â€“ 3A â€“ 6

Or 3A â€“ 2B = -6 â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ (2)

When equation (2) is subtracted from (1)

(3A â€“ B) â€“ (3A â€“ 2B) = 3 â€“ (-6)

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

By using the equation (1) we get,

3A â€“ 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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