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Question

If the length of a rectangle is increased by 20% and width is decreased by 20% ,what is the change in area of the rectangle?

unchanged

decreases by 4%

increases by 4%

increases by 5%

ANSWER : 2

Descrption

<pre> ধরি, আয়তের দৈর্ঘ্য  =  x 
                   প্রস্থ  =  y 
∴ ক্ষেত্রফল  =  xy 
20%  বৃদ্ধিতে দৈর্ঘ্য 
 =  <math xmlns = "http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>  +  </mo><mfrac><mn>20</mn><mn>100</mn></mfrac><mi>x</mi><mo>&#xA0;</mo><mspace linebreak = "newline"/><mo> = </mo><mo>(</mo><mn>1</mn><mo>  +  </mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>)</mo><mi>x</mi><mspace linebreak = "newline"/><mo> = </mo><mfrac><mn>5</mn><mn>6</mn></mfrac><mi>y</mi><mspace linebreak = "newline"/></math>
20%  হ্রাসে প্রস্থ 
 = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo> - </mo><mfrac><mn>20</mn><mn>100</mn></mfrac><mi>y</mi><mspace linebreak = "newline"/><mo> = </mo><mo>(</mo><mn>1</mn><mo> - </mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>)</mo><mi>y</mi><mspace linebreak = "newline"/><mo> = </mo><mfrac><mn>4</mn><mn>5</mn></mfrac><mi>y</mi><mspace linebreak = "newline"/></math>
∴ পরিবর্তিত ক্ষেত্রফল  = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mfrac><mn>6</mn><mn>5</mn></mfrac><mi>x</mi><mo>&#xA0;</mo><mo>&#xD7;</mo><mfrac><mn>4</mn><mn>5</mn></mfrac><mi>x</mi><mo>&#xA0;</mo><mspace linebreak = "newline"/><mo> = </mo><mfrac><mn>24</mn><mn>25</mn></mfrac><mi>x</mi><mi>y</mi><mo><</mo><mi>x</mi><mi>y</mi><mspace linebreak = "newline"/></math>
∴ শতকরা হ্রাস 
 = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mi>y</mi><mo> - </mo><mstyle displaystyle = "true"><mfrac><mn>24</mn><mn>25</mn></mfrac></mstyle><mi>x</mi><mi>y</mi></mrow><mrow><mi>x</mi><mi>y</mi></mrow></mfrac><mo>&#xD7;</mo><mn>100</mn><mo>%</mo><mspace linebreak = "newline"/><mo> = </mo><mo>(</mo><mn>1</mn><mo> - </mo><mfrac><mn>24</mn><mn>25</mn></mfrac><mo>)</mo><mo>&#xD7;</mo><mn>100</mn><mo>%</mo><mspace linebreak = "newline"/><mo> = </mo><mfrac><mn>1</mn><mn>25</mn></mfrac><mo>&#xD7;</mo><mn>100</mn><mo>%</mo><mspace linebreak = "newline"/><mo> = </mo><mn>4</mn><mo>%</mo><mo>&#xA0;</mo><mspace linebreak = "newline"/></math>
</pre>

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