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Question

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

A
55
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B
30
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C
115
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D
60
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Solution

The correct option is C 60
Let the original number of rows =x
Let the original number of students in each row =y
Total number of students in class = Number of students × Number of rows =xy
According to problem
Case 1
Total no of students =(y+1)(x2)=xy
xy2y+x2=xy
x2y=2 ...(1)
Case 2
Total no of students =(y1)(x+3)=xy
xy+3yx3=xy
x3y=3 ...(2)
Subtracting eq(1) from eq(2) we get
y=5
y=5
Putting the value of y in eq(1)
x2(5)=2
x=12
Hence we get x=12 and y=5
Total no. of students =xy=60

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