251. A number exceeds its two fifth by 75. The number is

1. 1. 125

   
   
   

   2. 112

   
   
   

   3. 100

   
   
   

   4. 150

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the number be x.
   According to the question,
   

   x −	2x	= 75
   	5

   
   

   ⇒	5x − 2x	= 75
   	5

   
   

   ⇒	3x	= 75
   	5

   
   

   ⇒  x =	75 × 5	= 125
   	3

   Correct Option: A

   Let the number be x.
   According to the question,
   

   x −	2x	= 75
   	5

   
   

   ⇒	5x − 2x	= 75
   	5

   
   

   ⇒	3x	= 75
   	5

   
   

   ⇒  x =	75 × 5	= 125
   	3

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252. Ram left 1/3 of his property to his widow and 3/5 of the remainder to his daughter. He gave the rest to his son who received Rs. 6,400. How much was his original property worth ?

1. 1. ₹ 16, 000

   
   
   

   2. ₹ 32, 000

   
   
   

   3. ₹ 24, 000

   
   
   

   4. ₹ 1, 600

   
   
   

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1. View Hint View Answer Discuss in Forum

   The original property with Ram = ₹ x (let)
   

   ∴  Wife’s share = Rs.	x
   	3

   
   Remaining property
   

   = x −	x	= ₹	2x
   	3		3

   
   

   Daughter’s share =	2x	×	3	= ₹	2x
   	3		5		5

   
   

   Son’s share =	2x	−	2x
   	3		5

   
   

   =	10x − 6x	= ₹	4x
   	15		15

   
   

   ∴	4x	= 6400
   	15

   
   ⇒  4x = 6400 × 15
   

   ⇒ x =	6400 × 15	= ₹ 24000
   	4

   
   

   Correct Option: C

   The original property with Ram = ₹ x (let)
   

   ∴  Wife’s share = Rs.	x
   	3

   
   Remaining property
   

   = x −	x	= ₹	2x
   	3		3

   
   

   Daughter’s share =	2x	×	3	= ₹	2x
   	3		5		5

   
   

   Son’s share =	2x	−	2x
   	3		5

   
   

   =	10x − 6x	= ₹	4x
   	15		15

   
   

   ∴	4x	= 6400
   	15

   
   ⇒  4x = 6400 × 15
   

   ⇒ x =	6400 × 15	= ₹ 24000
   	4

   
   

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253. 1	+	1	+	1	+	1	+	1	+	1	+	1	+	1	is equal to :
     20		30		42		56		72		90		110		132

1. 1. 1

      8

   
   
   

   2. 1

      7

   
   
   

   3. 1

      6

      
      

   
   
   

   4. 1

      10

   
   
   

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1. View Hint View Answer Discuss in Forum

   Expression =	1	+	1	+	1	+ .... +	1
   	20		30		42		132

   
   

   =	1	+	1	+	1	+ .... +	1
   	4 × 5		5 × 6		6 × 7		11 × 12

   
   

   1	−	1	+	1	−	1	+	1	−	1	+ .... +	1	+	1
   4		5		5		6		6		7		11		12

   
   

   =	1	−	1	=	3 − 1	=	2	=	1
   	4		12		12		12		6

   Correct Option: C

   Expression =	1	+	1	+	1	+ .... +	1
   	20		30		42		132

   
   

   =	1	+	1	+	1	+ .... +	1
   	4 × 5		5 × 6		6 × 7		11 × 12

   
   

   1	−	1	+	1	−	1	+	1	−	1	+ .... +	1	+	1
   4		5		5		6		6		7		11		12

   
   

   =	1	−	1	=	3 − 1	=	2	=	1
   	4		12		12		12		6

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254. 1 +	1	+	1	+	1	+	1	+	1	is equal to :
     	2		4		7		14		28

1. 1. 2

   
   
   

   2. 2.5

   
   
   

   3. 3

   
   
   

   4. 3.5

   
   
   

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1. View Hint View Answer Discuss in Forum

   ? = 1 +	1	+	1	+	1	+	1	+	1
   	2		4		7		14		28

   
   

   =	28 + 14 + 7 + 4 + 2 + 1
   	28

   
   

   =	28 + 28	= 2
   	28

   Correct Option: A

   ? = 1 +	1	+	1	+	1	+	1	+	1
   	2		4		7		14		28

   
   

   =	28 + 14 + 7 + 4 + 2 + 1
   	28

   
   

   =	28 + 28	= 2
   	28

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255. The value of
     

     1	+	1	+	1	+	1	+	1	+	1	is
     20		30		42		56		72		90

1. 1. 1

      10

   
   
   

   2. 3

      5

   
   
   

   3. 3

      20

   
   
   

   4. 7

      20

   
   
   

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1. View Hint View Answer Discuss in Forum

   5⁷¹ + 5⁷² + 5⁷³
   = 5⁷¹ (1 + 5 + 5²)
   = 5⁷¹ × 31 which is exactly divisible by 155.

   Correct Option: C

   5⁷¹ + 5⁷² + 5⁷³
   = 5⁷¹ (1 + 5 + 5²)
   = 5⁷¹ × 31 which is exactly divisible by 155.

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