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Q.

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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a

  the total number of students in the class is 36.

b

  the total number of students in the class is 35.

c

  the total number of students in the class is 42.

d

  the total number of students in the class is 51. 

answer is A.

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Detailed Solution

Given that the students of a class are made to stand in rows.
Also given, if 3 students are extra in a row, there would be 1 row less and if 3 students are less in a row, there would be 2 rows more.
Let us assume the number of rows be y and number of students in a row be x.
Total students of the class = Number of rows × Number of students in a row
Total students of the class = xy
When 3 student extra in a row and 1 row less, then
Total number of students = y1 x+3 .
xy= y1 x+3 xy=y x+3 1 x+3 xy=yx+3yx3 3yx3=0 3yx=3 x+3y=3 …………,...(1)
When 3 student less in a row and 2 row more, then
Total number of students = y+2 x3 .
xy= y+2 x3 xy=y x3 +2 x3 xy=xy3y+2x6 0=3y+2x6 2x3y=6 ………….. (2)
Multiply equation (1) by 2.
x+3y=3 2x+6y=6 ………………..(3)
Add equation (2) and (3).
2x3y+ 2x+6y =6+6 2x3y2x+6y=12 3y+6y=12 3y=12 y= 12 3 y=4
Put in equation (1).
x+3 4 =3 x+12=3 x=312 x=9 x=9
Since, number of students in class = xy.
Substitute x=9 and y=4 in above equation.
Number of students in class is,
=9×4 =36 Hence, the total number of students in the class is 36.
The correct option is (1).
 
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