111. 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 = ₹ x and second part = ₹ y.
   According to question,
   

   	x × 80	=	y × 60	+ 3
   	100		100

   
   

   ⇒	4x	=	3y	+ 3
   	5		5

   
   ⇒ 4x – 3y = 15 ....................(i)
   Again,
   

   	4y	=	9x	+ 6
   	5		10

   
   ⇒ 8y = 9x + 60
   ⇒ 8y – 9x = 60 ...............(ii)
   By equation (i) × 8 + (ii) × 3,
   

   	32x – 24y = 120 24y – 27x = 180
   	5x = 300 ⇒ x = 60

   
   From equation (i)
   4 × 60– 3y = 15
   ⇒ 3y = 240 – 15 = 225
   

   ⇒ y =	225	= 75
   	3

   
   ∴ x + y = 60 + 75 = 135

   Correct Option: C

   First part = ₹ x and second part = ₹ y.
   According to question,
   

   	x × 80	=	y × 60	+ 3
   	100		100

   
   

   ⇒	4x	=	3y	+ 3
   	5		5

   
   ⇒ 4x – 3y = 15 ....................(i)
   Again,
   

   	4y	=	9x	+ 6
   	5		10

   
   ⇒ 8y = 9x + 60
   ⇒ 8y – 9x = 60 ...............(ii)
   By equation (i) × 8 + (ii) × 3,
   

   	32x – 24y = 120 24y – 27x = 180
   	5x = 300 ⇒ x = 60

   
   From equation (i)
   4 × 60– 3y = 15
   ⇒ 3y = 240 – 15 = 225
   

   ⇒ y =	225	= 75
   	3

   
   ∴ x + y = 60 + 75 = 135

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112. A man invested 27,000 in
     

     12	1	%
     	2

     
     stock at 108, then his yield percentage is

1. 1. 18	3	%
      	4

   
   
   

   2. 11	31	%
      	54

   
   
   

   3. 15%

   
   
   

   4. 8	1	%
      	2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Value of ₹ 100 stock = ₹ 108
   

   ∵ Income on investing ₹ 108 = ₹	25
   	2

   
   ∴ Income on investment of ₹ 27000
   

   = ₹		25	× 27000		= ₹ 3125
   		2 × 108

   
   ∴ Gain per cent
   

   =	3125	× 100
   	27000

   
   

   	625	= 11	31	%
   	54		54

   Correct Option: B

   Value of ₹ 100 stock = ₹ 108
   

   ∵ Income on investing ₹ 108 = ₹	25
   	2

   
   ∴ Income on investment of ₹ 27000
   

   = ₹		25	× 27000		= ₹ 3125
   		2 × 108

   
   ∴ Gain per cent
   

   =	3125	× 100
   	27000

   
   

   	625	= 11	31	%
   	54		54

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113. The percentage of metals in a mine of lead ore is 60%. Now the percentage of silver is
     

     	1	%
     	2

     of metals and the rest is lead. If the mass of ore extracted from this mine is 8000 kg, the mass (in kg.) of lead is :

1. 1. 4763

   
   
   

   2. 4762

   
   
   

   3. 4764

   
   
   

   4. 4761

   
   
   

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1. View Hint View Answer Discuss in Forum

   Required mass of lead
   

   = 8000 ×	60	×		1 -	3
   	100				400

   
   

   = 8000 ×	60	×	397	= 4764 kg.
   	54		54

   Correct Option: C

   Required mass of lead
   

   = 8000 ×	60	×		1 -	3
   	100				400

   
   

   = 8000 ×	60	×	397	= 4764 kg.
   	54		54

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114. The sum of two positive numbers is 20% of the sum of their
     squares and 25% of the difference of their squares. If the numbers are x and y then,
     

     	x + y	is equal to
     	x2

1. 1. 1

      4

   
   
   

   2. 3

      8

   
   
   

   3. 1

      3

   
   
   

   4. 2

      9

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to the question,
   

   x + y = (x2 + y2) ×	1
   	5

   
   

   Again, x + y = (x2 + y2) ×	1
   	4

   
   

   ∴	x2 + y2	=	x2 - y2
   	5		4

   
   ⇒ 5x² – 5y² = 4x² + 4y²
   ⇒ 5x² – 4x² = 5y² + 4y²
   ⇒ x² = 9y²
   ⇒ x = 3y
   

   ∴	x + y	=	x2 + y2
   	x2		5x2

   
   

   =	9y2 + y2	=	10y2	=	2
   	5 × 9y2		45y2		9

   Correct Option: D

   According to the question,
   

   x + y = (x2 + y2) ×	1
   	5

   
   

   Again, x + y = (x2 + y2) ×	1
   	4

   
   

   ∴	x2 + y2	=	x2 - y2
   	5		4

   
   ⇒ 5x² – 5y² = 4x² + 4y²
   ⇒ 5x² – 4x² = 5y² + 4y²
   ⇒ x² = 9y²
   ⇒ x = 3y
   

   ∴	x + y	=	x2 + y2
   	x2		5x2

   
   

   =	9y2 + y2	=	10y2	=	2
   	5 × 9y2		45y2		9

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115. A man bought some eggs of which 10% are rotten. He gives 80% of the remainder to his neighbours. Now he is left out with 36 eggs. How many eggs he bought ?

1. 1. 40

   
   
   

   2. 100

   
   
   

   3. 200

   
   
   

   4. 72

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the total number of eggs bought be x.
   10% of eggs are rotten.
   ∴ Remaining eggs
   

   =	90x	=	9x
   	100		10

   
   After giving 80% of eggs to the neighbour,
   

   Remaining eggs =	9x × 20	=	9x
   	10 × 100		50

   
   According to the question
   

   	9x	= 36 ⇒ 9x = 36 × 50
   	50

   
   

   ⇒ x =	36 × 5	= 200
   	9

   Correct Option: C

   Let the total number of eggs bought be x.
   10% of eggs are rotten.
   ∴ Remaining eggs
   

   =	90x	=	9x
   	100		10

   
   After giving 80% of eggs to the neighbour,
   

   Remaining eggs =	9x × 20	=	9x
   	10 × 100		50

   
   According to the question
   

   	9x	= 36 ⇒ 9x = 36 × 50
   	50

   
   

   ⇒ x =	36 × 5	= 200
   	9

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