The length of a rectangle is increased by 60% :

The length of a rectangle is increased by 60% .By what percent would the width have to be decreased to maintain the same area ?

  1. 37 1/2%
  2. 60%
  3. 75%
  4. 66 2/3%
sanoopvil Newbie Asked on 23rd January 2016 in Maths.
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  • 1 Answer(s)

    Answer:  (1) 37  1/2%

    Explanation:-
    Let the length of a rectangle be X m and the breadth be Y m

    Then, the area of the rectangle = X Y m^2

    If the length of a rectangle is increased by 60%.
    Then, length of rectangle = X + X x 60/100
    X + 3 X/5
    = 8 X/5

    Let the width of new rectangle be Y1

    So, the area of new rectangle = 8 X x Y1/5
    = 8 X Y1/5  m^2

    The area should be same,
    Therefore, X Y = 8 X Y1/5
    Y1 = 5 Y/8

    Then, decrease in width = Y – Y 1 = Y – 5 Y/8
    = 3 Y/8

    Percentage of decrease = 3 Y x 100/8 Y
    = 75/2 => 37.5%

    Hence, the correct answer is option (1) 37 1/2%.

    Short Trick:-
    Require reduction = 60 x 100/160
    = 75/2%
    = 37  1/2%.

    Anurag Mishra Professor Answered on 23rd January 2016.
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