The students of a class are made to stand in rows. If number of students in each rows reduced by 2, the number of rows increases by 1 but if the number of students in each row is increased by 3, the number of rows is reduced by 1. Find the number of students in the class. Ans. 60
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Answer:
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
Explanation: