556. If the side of a square is increased by 25%, then its area is increased by :
     

1. 1. 25%
      

   
   
   

   2. 55%
      

   
   
   

   3. 40.5%
      

   
   
   

   4. 56.25%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 12,
   Let the side of a square is increased by x %, its area is increased by
   

   =		2x² +	x²		%
   			100

   
   Here, x = 25%
   

   ∴ Effective increase in area =		2 × 25 +	25 × 25		% = 56.26%
   			100

   Correct Option: D

   Using Rule 12,
   Let the side of a square is increased by x %, its area is increased by
   

   =		2x² +	x²		%
   			100

   
   Here, x = 25%
   

   ∴ Effective increase in area =		2 × 25 +	25 × 25		% = 56.26%
   			100

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557. If the radius of a circle is increased by 50%, its area is increased by :
     

1. 1. 125%
      

   
   
   

   2. 100%
      

   
   
   

   3. 75%
      

   
   
   

   4. 50%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 12,
   If the radius of circle is increased by x%, the area changes by
   

   =		2x +	x²		%
   			100

   
   

   =		2 × 50 +	50 × 50		% = 125%
   			100

   Correct Option: A

   Using Rule 12,
   If the radius of circle is increased by x%, the area changes by
   

   =		2x +	x²		%
   			100

   
   

   =		2 × 50 +	50 × 50		% = 125%
   			100

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558. If the length of a rectangle is increased by 20% and its breadth is decreased by 20%, then its area
     

1. 1. increases by 4%
      

   
   
   

   2. decreases by 4%
      

   
   
   

   3. decreases by 1%
      

   
   
   

   4. remains unchanged

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 10,
   

   Effective change in area =		x + y +	xy		%
   			100

   
   where x and y denote percentage change
   

   =		20 - 20 -	20 × 20		% = - 4%
   			100

   
   Hence, the area will decrease by 4%

   Correct Option: B

   Using Rule 10,
   

   Effective change in area =		x + y +	xy		%
   			100

   
   where x and y denote percentage change
   

   =		20 - 20 -	20 × 20		% = - 4%
   			100

   
   Hence, the area will decrease by 4%

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559. If each side of a rectangle is increased by 50%, its area will be increased by
     

1. 1. 50%
      

   
   
   

   2. 125%
      

   
   
   

   3. 100%
      

   
   
   

   4. 250%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 10,
   

   Effective increase =		50 + 50 +	50 × 50		% = 125%
   			100

   Correct Option: B

   Using Rule 10,
   

   Effective increase =		50 + 50 +	50 × 50		% = 125%
   			100

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560. If the altitude of a triangle is increased by 10% while its area remains same, its corresponding base will have to be decreased by
     

1. 1. 10 %
      

   
   
   

   2. 9 %
      

   
   
   

   3. 9	1	%
      	11

   
   
   

   4. 11	1	%
      	9

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the base of triangle be decreased by x%.
   According to the question,
   

   10 - x -	10x	= 0
   	100

   [∵ Area remains same]
   

   ⇒ x +	x	= 10
   	10

   
   

   ⇒	10x + x	= 10 ⇒	11x	= 10
   	10		10

   
   

   ⇒ x =	100	= 9	1	%
   	11		11

   Correct Option: C

   Let the base of triangle be decreased by x%.
   According to the question,
   

   10 - x -	10x	= 0
   	100

   [∵ Area remains same]
   

   ⇒ x +	x	= 10
   	10

   
   

   ⇒	10x + x	= 10 ⇒	11x	= 10
   	10		10

   
   

   ⇒ x =	100	= 9	1	%
   	11		11

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