MathematicsThe area of a rectangle gets reduced by 80 square units if its length is reduced by 5 units and the breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, the area is increased by 50 square units. Find the length and breadth of the rectangle respectively.

The area of a rectangle gets reduced by 80 square units if its length is reduced by 5 units and the breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, the area is increased by 50 square units. Find the length and breadth of the rectangle respectively.


  1. A
    40 units and 30 units
  2. B
    40 units and 50 units
  3. C
    50 units and 50 units
  4. D
    60 units and 50 units 

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    Solution:

    Given the area of rectangle gets reduced by 80 sq. units if its length is decreased by 5 units and breadth is increased by 2 units.
    If there is an increment in the length by 10 units and decrement in the breadth by 5 units, then area is increased by 50 square units.
    Let the length and breadth of rectangle be x and y respectively.
    We know the area of a rectangle is given by,
    A=length×breadth
    So, here we have,
    Area = x×y=xy
    According to the question, we have,
    xy(x5)(y+2) =80 xy(xy+2x5y10) =80 2x5y+70 =0.(1)  
    Similarly, from the second condition,
    (x+10)(y5)xy =50 (xy5x+10y50)xy =50 5x10y+100 =0 x2y+20 =0(2)  
    The solution of the equations a1x+b1y+c1=0 and a2x+b2y+c1=0 by cross multiplication method is given by the formula,
    xb1c2-b2c1=ya2c1-a1c2=1a1b2-a2b1
    Here, a1=2,b1=-5, c1=70, a2=1,b2=-2, c2=20.
    Using the cross-multiplication method to find the value of x and y,
    x-520-70-2=y701-(20)2=12(-2)-(1)(-5)
    x40=y30=11
    x=401= 40
    y=301=30
    Therefore, the length and breadth of the rectangle are 40 units and 30 units respectively.
    Hence, option (1) is correct.
     
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