456. If three-fifth of sixty percent of a number is 36, the number is

1. 1. 100

   
   
   

   2. 80

   
   
   

   3. 75

   
   
   

   4. 90

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the number be p.
   

   ∴	3	×	60	× p = 36
   	5		100

   
   

   Correct Option: A

   Let the number be p.
   

   ∴	3	×	60	× p = 36
   	5		100

   
   

   ⇒ p =	36 × 5 × 5	= 100
   	3 × 3

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457. A dozen pairs of socks quoted at ₹180 are available at discount of 20%. How many pairs of socks can be bought for ₹48?

1. 1. 3 pairs

   
   
   

   2. 4 pairs

   
   
   

   3. 2 pairs

   
   
   

   4. 5 pairs

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to question ,
   

   ∵ S.P. of a dozen pairs of socks =	180 × 80	= ₹144
   	100

   
   

   ∴ S.P. of 1 pair of socks =	144	= ₹12
   	12

   
   

   Correct Option: B

   According to question ,
   

   ∵ S.P. of a dozen pairs of socks =	180 × 80	= ₹144
   	100

   
   

   ∴ S.P. of 1 pair of socks =	144	= ₹12
   	12

   
   

   ∴ No. of pairs available for ₹ 48 =	48	= 4
   	12

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458. A box has 100 blue balls, 50 red balls, 50 black balls. 25% of blue balls and 50% of red balls are taken away. Percentage of black balls at present is

1. 1. 50%

   
   
   

   2. 25%

   
   
   

   3. 33	1	%
      	3

   
   
   

   4. 40%

   
   
   

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1. View Hint View Answer Discuss in Forum

   After taking away respective balls, Number of balls in the box = 75 + 25 + 50 = 150
   

   ∴ Percentage of black balls =	50	× 100
   	150

   
   

   Correct Option: C

   After taking away respective balls, Number of balls in the box = 75 + 25 + 50 = 150
   

   ∴ Percentage of black balls =	50	× 100
   	150

   
   

   Required answer =	100	= 33	1	%
   	3		3

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459. In a college, 40% of the students were allotted group A, 75% of the remaining were given group B and the remaining 12 students were given group C. Then the number of students who applied for the group is

1. 1. 100

   
   
   

   2. 60

   
   
   

   3. 80

   
   
   

   4. 92

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given that , Group A = 40%
   

   Group B =	60 × 75	= 45%
   	100

   
   Group C = 15%
   If the total number of students be p, then
   

   	p × 15	= 12
   	100

   
   

   Correct Option: C

   Given that , Group A = 40%
   

   Group B =	60 × 75	= 45%
   	100

   
   Group C = 15%
   If the total number of students be p, then
   

   	p × 15	= 12
   	100

   
   

   ⇒ p =	12 × 100	= 80
   	15

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460. A number is divided into two parts in such a way that 80% of 1st part is 3 more than 60% of 2nd part and 80% of 2nd part is 6 more than 90% of the 1st part. Then the number is

1. 1. 125

   
   
   

   2. 130

   
   
   

   3. 135

   
   
   

   4. 145

   
   
   

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1. View Hint View Answer Discuss in Forum

   First part = p and second part = q.
   

   ∴	p × 80	=	q × 60
   	100		100

   
   

   ⇒	4p	=	3q	+ 3
   	5		5

   
   ⇒ 4p – 3q = 15 ...(i)
   Again,
   

   	4q	=	9p	+ 6
   	5		10

   
   ⇒ 8q = 9p + 60
   ⇒ 8q – 9p = 60 ...(ii)
   By equation (i) × 8 + (ii) × 3,
   32p – 24q = 120
   24q – 27p = 180
   --------------------------
   5p = 300 ⇒ p = 60
   

   Correct Option: C

   First part = p and second part = q.
   

   ∴	p × 80	=	q × 60
   	100		100

   
   

   ⇒	4p	=	3q	+ 3
   	5		5

   
   ⇒ 4p – 3q = 15 ...(i)
   Again,
   

   	4q	=	9p	+ 6
   	5		10

   
   ⇒ 8q = 9p + 60
   ⇒ 8q – 9p = 60 ...(ii)
   By equation (i) × 8 + (ii) × 3,
   32p – 24q = 120
   24q – 27p = 180
   --------------------------
   5p = 300 ⇒ p = 60
   From equation (i)
   4 × 60– 3q = 15
   ⇒ 3q = 240 – 15 = 225
   

   ⇒ q =	225	= 75
   	3

   
   ∴ p + q = 60 + 75 = 135

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