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Question

Students of a class are made to stand in rows. If one student is extra in each row, there would be 2 rows less. If one students is less in each row, there would be 3 rows more. Find the number of students in the class.

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Solution

Let the number of rows be x and number of students in one row be y.
therefore total number of students =xy.
if one student is extra in a row, there will be 2 rows less.
the number of students in 1 row =y+1 and the number of rows =x2.
therefore the number of students =(x2)(y+1)
(x2)(y+1)=xy
xy2y+x2=xy
x2y=2..........(1)
if 1 student is less in a row there would be 3 rows more.
therefore
(y1)(x+3)=xy
xyx+3y3=xy
x+3y=3..........(2)
adding equation (1) and equation (2):
y=5
and x2×5=2
x10=2
x=10+2=12
thus the number of students in the class =xy=12×5=60

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