# 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 ?

- 37 1/2%
- 60%
- 75%
- 66 2/3%

**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%.