Question

customers are asked to stand in the lines. if one customer is extra in a line , then there would be two less lines . if one customer is less in line , there would be three more lines . find number of customers

Answer 1

Let the number of scustomers = x.

Let the number of customer per row = y originally.

Hence, total number of rows =xy
i) If the number of customer per row is 1 extra, then, number of rows =x(y+1)=(xy)−2 (2 rows less than original number of rows)
⇒x(y+1)=(x−2y)y⇒xy=(x−2y)(y+1)=xy−2y2+x−2y⇒x=2y(y+1)……(a)
ii) If the number per row is 1 less, then the number of rows =x(y−1)=(xy)+3
⇒x(y−1)=(x+3y)y⇒xy=(y−1)(x+3y)⇒xy=xy−x+3y2−3y⇒x=3y(y−1)……(b)
From (a) and (b)
2y(y+1)=3y(y−1)⇒2y+2=3y−3⇒y=5⇒x=3×5(5−1)=60
So the total number of customer = 60

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