326. The difference of two numbers is 45% of their sum. The ratio of the larger number to the smaller number is

1. 1. 20 : 9

   
   
   

   2. 9 : 20

   
   
   

   3. 29 : 11

   
   
   

   4. 11 : 29

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the numbers be p and q and p is greater than q.
   Then p – q = 45% of (p + q)
   

   ⇒ p – q =	45	(p + q)
   	100

   
   

   ⇒ p – q =	9	(p + q)
   	20

   
   ⇒ 20p – 20q = 9p + 9q
   

   Correct Option: C

   Let the numbers be p and q and p is greater than q.
   Then p – q = 45% of (p + q)
   

   ⇒ p – q =	45	(p + q)
   	100

   
   

   ⇒ p – q =	9	(p + q)
   	20

   
   ⇒ 20p – 20q = 9p + 9q
   ⇒ 20p – 9q = 20q + 9q
   ⇒ 11p = 29q
   

   ⇒	p	=	29	or 29 : 11
   	q		11

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327. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is

1. 1. 2 : 5

   
   
   

   2. 3 : 5

   
   
   

   3. 4 : 5

   
   
   

   4. 6 : 7

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the third number be 100.
   ∴ First number = 120
   Second number = 150
   

   Correct Option: C

   Let the third number be 100.
   ∴ First number = 120
   Second number = 150
   

   ∴ Required ratio =	120	=	4	or 4 : 5
   	150		5

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328. Two numbers are in the ratio 2 : 3. If 20% of the smaller number added to 20 is equal to the sum of 10% of the larger number and 25, then the smaller number is

1. 1. 100

   
   
   

   2. 160

   
   
   

   3. 180

   
   
   

   4. 200

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the numbers be 2k and 3k.
   According to the question,
   

   			20	× 2k		+ 20
   			100

   
   

   =			10	× 3k		+ 25
   			100

   
   

   ⇒	2k	+ 20 =	3k	+ 25
   	5		10

   
   

   Correct Option: A

   Let the numbers be 2k and 3k.
   According to the question,
   

   			20	× 2k		+ 20
   			100

   
   

   =			10	× 3k		+ 25
   			100

   
   

   ⇒	2k	+ 20 =	3k	+ 25
   	5		10

   
   

   ⇒	2k	-	3k	= 25 - 20
   	5		10

   
   

   ⇒	4k - 3k	= 5 ⇒ k = 50
   	10

   
   ∴ The smaller number = 2k = 100

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329. The ratio of the number of boys to that of girls in a school is 4 : 1. If 75% of boys and 70% of the girls are scholarship holders, then the percentage of students who do not get scholarship is

1. 1. 50%

   
   
   

   2. 28%

   
   
   

   3. 75%

   
   
   

   4. 26%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the number of boys and girls be 4k and k respectively.
   

   Number of boys who hold scholarship =	75	× 4k = 3k
   	100

   
   

   and number of girls who hold scholarship =	70 + k	=	7k
   	100		10

   
   

   Number of students who do not hold scholarship = 5k - 3k -	7k	= 2k -	7k
   	10		10

   
   

   Number of students who do not hold scholarship =	20k - 7k	=	13k
   	10		10

   
   

   Correct Option: D

   Let the number of boys and girls be 4k and k respectively.
   

   Number of boys who hold scholarship =	75	× 4k = 3k
   	100

   
   

   and number of girls who hold scholarship =	70 + k	=	7k
   	100		10

   
   

   Number of students who do not hold scholarship = 5k - 3k -	7k	= 2k -	7k
   	10		10

   
   

   Number of students who do not hold scholarship =	20k - 7k	=	13k
   	10		10

   
   The required percentage

   	13k
   =	10	× 100
   	5k

   
   

   The required percentage =	13k	× 100 = 26%
   	10 × 5k

   
   

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330. The ratio of the number of boys and girls in a college is 3 : 2. If 20% of boys and 25% of girls are adults, the percentage of those students who are not adults, is

1. 1. 58%

   
   
   

   2. 67.5%

   
   
   

   3. 78%

   
   
   

   4. 82.5%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the number of boys and girls in the college be 3k and 2k respectively.
   

   Number of minor boys = 3k ×	80	=	12k
   	100		5

   
   

   Number of minor girls = 2k ×	75	=	3k
   	100		2

   
   

   Total number of minor students =	12k	+	3k
   	5		2

   
   

   Correct Option: C

   Let the number of boys and girls in the college be 3k and 2k respectively.
   

   Number of minor boys = 3k ×	80	=	12k
   	100		5

   
   

   Number of minor girls = 2k ×	75	=	3k
   	100		2

   
   

   Total number of minor students =	12k	+	3k
   	5		2

   
   

   Total number of minor students =	24k + 15k	=	39k
   	10		10

   
   

   Required percentage =	39k	× 100 = 78%
   	10 × 5k

   
   (As total students = 3k + 2k = 5k)

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