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 C60 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)(x−2)=xy ⇒xy−2y+x−2=xy ⇒x−2y=2 ...(1) Case 2 Total no of students =(y−1)(x+3)=xy ⇒xy+3y−x−3=xy ⇒x−3y=−3 ...(2) Subtracting eq(1) from eq(2) we get −y=−5 ⇒y=5 Putting the value of y in eq(1) x−2(5)=2 ⇒x=12 Hence we get x=12 and y=5 Total no. of students =xy=60