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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