In a rectangle, the length is increased by 10%, and the width is decre

Question

In a rectangle, the length is increased by 10%, and the width is decreased by 10%. What percentage is the reduced area of the rectangle? 6.12 PS.png A. 1{%} B. 5{%} C. 10{%} D. 15{%} E. 17{%}

yashikaaggarwal · Answer

MathRevolution  Sir I guess % sign is missing after 10, because there is no other case in which the change in area can be calculated. Kindly re-evaluate the question.

QuantMadeEasy · Answer

It must be 10% increase and 10% decrease, then the OA is 1% decrease. Kindly edit

yashikaaggarwal · Answer

Let the length of original rectangle be L and breadth be B
Area = L*B -----------(1)

Length of changed rectangle = 1.1*L
Breadth of changed rectangle = 0.9*B
Area = 1.1*L*0.9*B = 0.99*L*B

Reduced area of rectangle = original area - changed area
=L*B - 0.99*L*B => 0.01*L*B

The percentage change = 0.01*L*B*100/1 => 1

Answer is A

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MathRevolution · Answer

=>

Assume  a = AD  and  b = AB  are the lengths of the two sides of rectangle  ABCD , as shown in the figure.

Then the area of the rectangle  ABCD  is  ab.

Then the area of the rectangle  AB’C’D’  is  a(1 - 0.1)·b(1 + 0.1) = ab(1 - 0.01)  after the sides change.

Thus, the area is decreased by  1%.

Therefore, A is the answer.
Answer: A

In a rectangle, the length is increased by 10%, and the width is decre

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In a rectangle, the length is increased by 10%, and the width is decre

Prep Toolkit

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