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 =x−2.
therefore the number of students =(x−2)(y+1)
∴(x−2)(y+1)=xy
→xy−2y+x−2=xy
→x−2y=2..........(1)
if 1 student is less in a row there would be 3 rows more.
therefore
(y−1)(x+3)=xy
→xy−x+3y−3=xy
→−x+3y=3..........(2)
adding equation (1) and equation (2):
y=5
and x−2×5=2
x−10=2
→x=10+2=12
thus the number of students in the class =xy=12×5=60