346. In a school having roll strength 286, the ratio of boys and girls is 8 : 5. If 22 more girls get admitted into the school, the ratio of boys and girls becomes

1. 1. 12 : 7

   
   
   

   2. 10 : 7

   
   
   

   3. 8 : 7

   
   
   

   4. 4 : 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Initially number of boys
   

   =	8	× 286 =	8	× 286 = 176
   	8 + 5		13

   
   ∴  Number of girls
   

   =	5	× 286 = 110
   	13

   
   22 more girls get admitted.
   ∴  Required ratio
   

   =	176	=	176	=	4
   	110 + 22		132		3

   
   = 4 : 3

   Correct Option: D

   Initially number of boys
   

   =	8	× 286 =	8	× 286 = 176
   	8 + 5		13

   
   ∴  Number of girls
   

   =	5	× 286 = 110
   	13

   
   22 more girls get admitted.
   ∴  Required ratio
   

   =	176	=	176	=	4
   	110 + 22		132		3

   
   = 4 : 3

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347. The ratio of the number of ladies to that of gents at a party was 3 : 2. When 20 more gents joined the party, the ratio was reversed. The number of ladies present at the party was

1. 1. 36

   
   
   

   2. 32

   
   
   

   3. 24

   
   
   

   4. 16

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the number of ladies and gents be 3x and 2x respectively.
   According to the question,
   

   3x	=	2
   2x + 20		3

   
   ⇒  9x = 4x + 40 ⇒ 5x = 40
   ⇒  9x = 4x + 40 ⇒ 5x = 40
   ⇒  x = 8
   ∴  Number of ladies = 3x
   = 3 × 8 = 24

   Correct Option: C

   Let the number of ladies and gents be 3x and 2x respectively.
   According to the question,
   

   3x	=	2
   2x + 20		3

   
   ⇒  9x = 4x + 40 ⇒ 5x = 40
   ⇒  9x = 4x + 40 ⇒ 5x = 40
   ⇒  x = 8
   ∴  Number of ladies = 3x
   = 3 × 8 = 24

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348. The ratio of the number of boys and that of girls in a school having 504 students is 13 :11. What will be the new ratio if 3 more girls are admitted?

1. 1. 7 : 6

   
   
   

   2. 6 : 7

   
   
   

   3. 10 :11

   
   
   

   4. 13 :14

   
   
   

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1. View Hint View Answer Discuss in Forum

   Number of boys
   

   =	13	× 504
   	13 + 11

   
   

   =	13	× 504 = 273
   	24

   
   Number of girls
   = 504–273 = 231
   3 girls are admitted.
   ∴  Required ratio = 273 : 234
   = 7 : 6

   Correct Option: A

   Number of boys
   

   =	13	× 504
   	13 + 11

   
   

   =	13	× 504 = 273
   	24

   
   Number of girls
   = 504–273 = 231
   3 girls are admitted.
   ∴  Required ratio = 273 : 234
   = 7 : 6

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349. The students in three classes are in the ratio 2 : 3 : 5. If 20 students are increased in each
     class, the ratio changes to 4 : 5 : 7. Originally the total number of students was :

1. 1. 50

   
   
   

   2. 90

   
   
   

   3. 100

   
   
   

   4. 150

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the original number of students in three classes be 2x, 3x and 5x respectively.
   As given,
   

   2x + 20	=	4
   3x + 20		5

   
   ⇒  10x + 100 = 12x + 80
   ⇒  12x – 10x = 100 – 80
   ⇒  2x = 20
   

   ⇒  x =	20	= 10
   	2

   
   ∴  Total number of students originally
   = 2x + 3x + 5x = 10x
   = 10 × 10 = 100

   Correct Option: C

   Let the original number of students in three classes be 2x, 3x and 5x respectively.
   As given,
   

   2x + 20	=	4
   3x + 20		5

   
   ⇒  10x + 100 = 12x + 80
   ⇒  12x – 10x = 100 – 80
   ⇒  2x = 20
   

   ⇒  x =	20	= 10
   	2

   
   ∴  Total number of students originally
   = 2x + 3x + 5x = 10x
   = 10 × 10 = 100

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350. The ratio of number of boys to that of girls in a group becomes 2:1 when 15 girls leave. But, afterwards, when 45 boys also leave, the ratio becomes 1 : 5. Originally the number of girls in
     the group was

1. 1. 20

   
   
   

   2. 30

   
   
   

   3. 40

   
   
   

   4. 50

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the original number of boys and girls be x and y respectively.
   Then
   

   x	=	2
   y − 15		1

   
   ⇒  x = 2y – 30       ....(i)
   

   Again,	x − 45	=	1
   	y − 15		5

   
   ⇒  5x – 225 = y – 15
   ⇒  5x = y – 15 + 225
   ⇒  5 (2y–30) = y + 210 [From equation (i)]
   ⇒  10y – 150 = y + 210
   ⇒  10y – y = 210 + 150
   ⇒  9y = 360
   

   ⇒  y =	360	= 40
   	9

   Correct Option: C

   Let the original number of boys and girls be x and y respectively.
   Then
   

   x	=	2
   y − 15		1

   
   ⇒  x = 2y – 30       ....(i)
   

   Again,	x − 45	=	1
   	y − 15		5

   
   ⇒  5x – 225 = y – 15
   ⇒  5x = y – 15 + 225
   ⇒  5 (2y–30) = y + 210 [From equation (i)]
   ⇒  10y – 150 = y + 210
   ⇒  10y – y = 210 + 150
   ⇒  9y = 360
   

   ⇒  y =	360	= 40
   	9

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