156. If 60% of students in a school are boys and the total number of girls in the school is 460, find the number of boys in the school.

1. 1. 680

   
   
   

   2. 690

   
   
   

   3. 700

   
   
   

   4. 720

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the total number of students be x.
   Given,Number of boys
   

   =	60	x .........(i)
   	100

   
   Number of girls = 460
   ⇒ Number of boys = x – 460 ......... (ii)
   From equations (i) and (ii),
   

   ⇒ x – 460 =	60x
   	100

   
   

   ⇒460 =	40	x
   	100

   
   

   ⇒ x =	460 × 100	= 1150
   	40

   
   ∴ Number of boys = 1150 – 460 = 690.

   Correct Option: B

   Let the total number of students be x.
   Given,Number of boys
   

   =	60	x .........(i)
   	100

   
   Number of girls = 460
   ⇒ Number of boys = x – 460 ......... (ii)
   From equations (i) and (ii),
   

   ⇒ x – 460 =	60x
   	100

   
   

   ⇒460 =	40	x
   	100

   
   

   ⇒ x =	460 × 100	= 1150
   	40

   
   ∴ Number of boys = 1150 – 460 = 690.

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157. In a direct election between two contestants for the post of secretary, 4% of the total votes cast are declared to be illegal. One contestant secures 55% of the valid votes and wins with a majority of 240 votes, find the total number of votes cast.

1. 1. 3500

   
   
   

   2. 2400

   
   
   

   3. 2200

   
   
   

   4. 2500

   
   
   

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1. View Hint View Answer Discuss in Forum

   Suppose total number of votes cast = x.
   ∴ Number of illegal votes = 4% of
   

   x =	4x	=	x
   	100		25

   
   ∴ Number of valid votes
   

   = x –	x	=	25x - x	=	24x
   	25		25		25

   
   Votes secured by the contestant who is defeated
   

   =	24x	–	24x	×	55
   	25		25		100

   
   

   =	24x			1 -	55
   	25				100

   
   

   =	24x	×	45
   	25		100

   
   According to the question,
   

   =	24x	×	55	- 240
   	25		100

   
   

   =	24x	×	45
   	25		100

   
   

   ⇒	24x			55	-	45		= 240
   	25			100		100

   
   

   ⇒	24x	.	10	= 240
   	25		100

   
   

   =	24x	= 240
   	250

   
   

   ⇒ x =	250 × 240	= 2500
   	24

   
   ∴ Total number of votes cast = 2500

   Correct Option: D

   Suppose total number of votes cast = x.
   ∴ Number of illegal votes = 4% of
   

   x =	4x	=	x
   	100		25

   
   ∴ Number of valid votes
   

   = x –	x	=	25x - x	=	24x
   	25		25		25

   
   Votes secured by the contestant who is defeated
   

   =	24x	–	24x	×	55
   	25		25		100

   
   

   =	24x			1 -	55
   	25				100

   
   

   =	24x	×	45
   	25		100

   
   According to the question,
   

   =	24x	×	55	- 240
   	25		100

   
   

   =	24x	×	45
   	25		100

   
   

   ⇒	24x			55	-	45		= 240
   	25			100		100

   
   

   ⇒	24x	.	10	= 240
   	25		100

   
   

   =	24x	= 240
   	250

   
   

   ⇒ x =	250 × 240	= 2500
   	24

   
   ∴ Total number of votes cast = 2500

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158. 1. If 80% of A = 50% of B and B = y % of A, then the value of y is :

1. 1. 400

   
   
   

   2. 300

   
   
   

   3. 160

   
   
   

   4. 150

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to question
   

   A ×	80	= B ×	50
   	100		100

   
   

   ∴ B =	A × 80	= 1.6A
   	50

   
   ∴ B = 160% of A
   

   Correct Option: C

   According to question
   

   A ×	80	= B ×	50
   	100		100

   
   

   ∴ B =	A × 80	= 1.6A
   	50

   
   ∴ B = 160% of A
   ∴ y = 160
   Hence , the value of y is 160 .

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159. If x is 80% of y, what percent of y is x ?

1. 1. 75%

   
   
   

   2. 80%

   
   
   

   3. 100%

   
   
   

   4. 125%

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to question,
   

   y =	100 × 100	of x
   	80

   
   

   Correct Option: D

   According to question,
   

   y =	100 × 100	of x
   	80

   
   ∴ y = 125% of x

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160. If 8% of p is the same as 4% of q, then 20% of p is the same as:

1. 1. 10% of q

   
   
   

   2. 16% of q

   
   
   

   3. 80% of q

   
   
   

   4. 50% of q

   
   
   

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1. View Hint View Answer Discuss in Forum

   As per the given question,
   

   	8p	=	4q
   	100		100

   
   

   Correct Option: A

   As per the given question,
   

   	8p	=	4q
   	100		100

   
   ⇒ q = 2p
   ∴ 20% of p = 10% of q .

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