61. The tax imposed on an article is decreased by 10% and its consumption increases by 10%. Find the percentage change in revenue from it.

1. 1. 10% increase

   
   
   

   2. 2% decrease

   
   
   

   3. 1% decrease

   
   
   

   4. 11% increase

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 3
   Tricky approach
   Required change
   

   =	(10)2	% decrease = 1% decrease
   	100

   Correct Option: C

   Using Rule 3
   Tricky approach
   Required change
   

   =	(10)2	% decrease = 1% decrease
   	100

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62. The numerator of a fraction is increased by 20% and denominator is decreased by 20%.
    

    The value of the fraction becomes	4
    	5

    
    The original fraction is

1. 1. 	2
      	3

   
   
   

   2. 	8
      	15

   
   
   

   3. 	7
      	11

   
   
   

   4. 	4
      	5

   
   
   

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1. View Hint View Answer Discuss in Forum

   Original fraction =	x
   	y

   
   

   ∴	120	x	=
   	100			4
   	y ×	80		5
   		100

   
   

   ⇒	120x	=	4
   	80y		5

   
   

   ⇒	6x	=	4
   	4y		5

   
   

   ⇒	x	=	4	×	4	=	8
   	y		5		6		15

   Correct Option: B

   Original fraction =	x
   	y

   
   

   ∴	120	x	=
   	100			4
   	y ×	80		5
   		100

   
   

   ⇒	120x	=	4
   	80y		5

   
   

   ⇒	6x	=	4
   	4y		5

   
   

   ⇒	x	=	4	×	4	=	8
   	y		5		6		15

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63. If the numerator of a fraction is increased by 20% and the denominator is decreased by 5%,
    

    the value of the new fraction becomes	5	.
    	2

    
    The original fraction is

1. 1. 24

      19

   
   
   

   2. 3

      18

   
   
   

   3. 95

      48

   
   
   

   4. 48

      95

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let original fraction be	x
   	y

   
   According to the question,
   

   	120	x	=
   	100			5
   	95y			2
   	100

   
   

   ⇒	120x	=	5
   	95y		2

   
   

   ⇒	x	=	5	×	95	=	95
   	y		2		120		48

   Correct Option: C

   Let original fraction be	x
   	y

   
   According to the question,
   

   	120	x	=
   	100			5
   	95y			2
   	100

   
   

   ⇒	120x	=	5
   	95y		2

   
   

   ⇒	x	=	5	×	95	=	95
   	y		2		120		48

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64. If a number is increased by 25% and the resulting number is decreased by 25%. then the percentage increase or decrease finally is

1. 1. no change

   
   
   

   2. decreased by 6	1	%
      	4

   
   
   

   3. increased by 6	1	%
      	4

   
   
   

   4. increased by 6%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 4,
   Effective value
   

   =		x + y +	xy		%
   			100

   
   

   =		25 - 25 -	25 × 25		%
   			100

   
   [Here, x = 25, y = –25]
   

   = –6.25% = 6	1	% decreased
   	4

   
   (Negative value shows decrease)

   Correct Option: B

   Using Rule 4,
   Effective value
   

   =		x + y +	xy		%
   			100

   
   

   =		25 - 25 -	25 × 25		%
   			100

   
   [Here, x = 25, y = –25]
   

   = –6.25% = 6	1	% decreased
   	4

   
   (Negative value shows decrease)

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65. The sum of two numbers is 520. If the bigger number is decreased by 4% and the smaller number is increased by 12%, then the numbers obtained are equal. The smaller number is

1. 1. 280

   
   
   

   2. 210

   
   
   

   3. 240

   
   
   

   4. 300

   
   
   

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1. View Hint View Answer Discuss in Forum

   Larger number = x and smaller number = 520 – x
   

   ∴	96x	=	(520 - x)	× 112
   	100		100

   
   ⇒ 96x = 520 × 112 – 112x
   ⇒ 112x + 96x = 520 × 112
   ⇒ 208x = 520 × 112
   

   ⇒ x =	520 × 112	= 280
   	208

   
   ∴ Smaller number
   = 520 – 280 = 240

   Correct Option: C

   Larger number = x and smaller number = 520 – x
   

   ∴	96x	=	(520 - x)	× 112
   	100		100

   
   ⇒ 96x = 520 × 112 – 112x
   ⇒ 112x + 96x = 520 × 112
   ⇒ 208x = 520 × 112
   

   ⇒ x =	520 × 112	= 280
   	208

   
   ∴ Smaller number
   = 520 – 280 = 240

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