276. The sum of the numerator and denominator of a positive fraction is 11. If 2 is added to both numerator and denominator, the fraction is increased by 1/24.The difference of numerator and denominator of the fraction is

1. 1. 5

   
   
   

   2. 3

   
   
   

   3. 1

   
   
   

   4. 9

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let numerator be x, then denominator = 11 – x.
   

   ∴  Fraction =	x
   	11 − x

   
   

   Again,	x + 2
   	11 − x + 2

   
   

   =	x	+	1
   	11 − x		24

   
   

   ⇒	x + 2	+	x	=	1
   	13 − x		11 − x		24

   
   

   ⇒	11x − x2 + 22 − 2x − 13x + x2	=	1
   	(13 − x )(11 − x)		24

   
   ⇒  528 – 96x = 143 – 24x + x²
   ⇒  x² + 72x – 385 = 0
   ⇒  x² + 77x – 5x – 385 = 0
   ⇒  x (x + 77) – 5 (x + 77) = 0
   ⇒  (x – 5) (x + 77) = 0 ⇒ x = 5
   ∴  Denominator = 11 – 5 = 6
   ∴  Difference = 6 – 5 = 1

   Correct Option: C

   Let numerator be x, then denominator = 11 – x.
   

   ∴  Fraction =	x
   	11 − x

   
   

   Again,	x + 2
   	11 − x + 2

   
   

   =	x	+	1
   	11 − x		24

   
   

   ⇒	x + 2	+	x	=	1
   	13 − x		11 − x		24

   
   

   ⇒	11x − x2 + 22 − 2x − 13x + x2	=	1
   	(13 − x )(11 − x)		24

   
   ⇒  528 – 96x = 143 – 24x + x²
   ⇒  x² + 72x – 385 = 0
   ⇒  x² + 77x – 5x – 385 = 0
   ⇒  x (x + 77) – 5 (x + 77) = 0
   ⇒  (x – 5) (x + 77) = 0 ⇒ x = 5
   ∴  Denominator = 11 – 5 = 6
   ∴  Difference = 6 – 5 = 1

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277. A fraction having denominator 30 and lying between 5/8 and 7/11 is -

1. 1. 18

      30

      
      

   
   
   

   2. 19

      30

   
   
   

   3. 20

      30

      
      

   
   
   

   4. 21

      30

   
   
   

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1. View Hint View Answer Discuss in Forum

   5	= 0.625 ;	7	= 0.636
   8		11

   
   

   20	= 0.666...;	19	= 0.633...
   30		30

   
   

   Correct Option: B

   5	= 0.625 ;	7	= 0.636
   8		11

   
   

   20	= 0.666...;	19	= 0.633...
   30		30

   
   

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278. How many 1/6 of together make

     41	2	?
     	3

1. 1. 125

   
   
   

   2. 150

   
   
   

   3. 250

   
   
   

   4. 350

   
   
   

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1. View Hint View Answer Discuss in Forum

   Required answer
   

   125/3	=	125	× 6 = 250
   1/6		3

   
   

   Correct Option: C

   Required answer
   

   125/3	=	125	× 6 = 250
   1/6		3

   
   

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279. A man spends	1	th of his income on food	2	rd of it on house rent and
     	4		3

     the remaining income which is ₹ 630 on other commodities. Find his house rent.

1. 1. 5040

   
   
   

   2. 3520

   
   
   

   3. 4890

   
   
   

   4. 4458

   
   
   

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1. View Hint View Answer Discuss in Forum

   Suppose total income = ₹ p
   

   ∴  p −	p	−	2p	= 630
   	4		3

   
   

   p	= 630   ∴ p = 7560
   12

   
   

   Correct Option: A

   Suppose total income = ₹ p
   

   ∴  p −	p	−	2p	= 630
   	4		3

   
   

   p	= 630   ∴ p = 7560
   12

   
   

   ∴  House rent =	2	× 7560 = ₹ 5040
   	3

   
   

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280. A tree increases annually by	1	th of its height. By how much will it
     8

     increase after 2 years, if it stands today 64 cm high?

1. 1. 72 cm

   
   
   

   2. 74 cm

   
   
   

   3. 75 cm

   
   
   

   4. 81 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to question ,
   

   Height of tree after 1 year = 64 + 64 ×	1	= 72 cm
   	8

   
   

   Height of tree after 2 years = 72 + 72 ×	1
   	8

   
   

   Correct Option: D

   According to question ,
   

   Height of tree after 1 year = 64 + 64 ×	1	= 72 cm
   	8

   
   

   Height of tree after 2 years = 72 + 72 ×	1
   	8

   
   Height of tree after 2 years = 72 + 9 = 81 cm

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