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Question

# If the length of a rectangle is decreased by 40% and the breadth is increased by 30%, then find the % change in the area of the rectangle.

A
22% Increase
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B
22% Decrease
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C
10% Decrease
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D
No change
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Solution

## The correct option is B 22% DecreaseLet x be the length and y be the breadth of the rectangle.The original area of the rectangle will be xy.After 40% decrease in the length, length of the new rectangle will be,x′=x(1−40100)=35xAfter 30% increase in the length, length of the new rectangle will be,y′=y(1+30100)=1310yArea of new rectangle=x′y′=3x5×13y10=39xy50Percentage change=(39xy50−xy)xy×100=−22%Here negative sign indicates that the area of the final rectangle is less than the original rectangle which means a 22% decrease in the area of the rectangle takes place.

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