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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

Q4.    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.

Answers (1)

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Let the number of rows be x and number of students in a row be y.
Total number of students in the class = Number of rows * Number of students in a row
                                                           =xy

Now, According to the question,

\\xy = (x - 1) (y + 3) \\\Rightarrow xy= xy - y + 3x - 3 \\\Rightarrow 3x - y - 3 = 0 \\ \Rightarrow 3x - y = 3 ...... ... (1)

 Also,

   \\xy=(x+2)(y-3)\\\Rightarrow xy = xy + 2y - 3x - 6 \\ \Rightarrow 3x - 2y = -6 ... (2)
Subtracting equation (2) from (1), we get:
y=9
Substituting the value of y in equation (1), we obtain:
\\3x - 9 = 3 \\\Rightarrow 3x = 9 + 3 = 12 \\\Rightarrow x = 4
Hence,
The number of rows is 4 and Number of students in a row is 9.

Total number of students in a class

:xy=(4)(9)=36

Hence there is 36 number of students in the class.

Posted by

Pankaj Sanodiya

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