106. The average monthly salary of 19 members of a group is Rs. 16000. If one more member whose monthly salary is Rs. 20000 joins the group, then the average salary of the group is
     

1. 1. Rs. 18250
      

   
   
   

   2. Rs. 16200
      

   
   
   

   3. Rs. 18000
      

   
   
   

   4. Rs. 16250

   
   
   

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1. View Hint View Answer Discuss in Forum

   The average monthly salary of 19 members of a group = Rs. 16000.
   A member whose monthly salary = Rs. 20000
   

   Required average = Rs.		16000 × 19 + 20000
   		20

   
   

   Required average = Rs.		304000 + 20000
   		20

   
   

   Required average = Rs.		324000
   		20

   
   Required average = Rs. 16200
   Second method to solve this question ,
   Difference = Rs. (20000 – 16000) = Rs. 4000
   

   Correct Option: B

   The average monthly salary of 19 members of a group = Rs. 16000.
   A member whose monthly salary = Rs. 20000
   

   Required average = Rs.		16000 × 19 + 20000
   		20

   
   

   Required average = Rs.		304000 + 20000
   		20

   
   

   Required average = Rs.		324000
   		20

   
   Required average = Rs. 16200
   Second method to solve this question ,
   Difference = Rs. (20000 – 16000) = Rs. 4000
   

   ∴ Increase in average =	4000
   	20

   
   Increase in average = Rs. 200
   ∴ Required average = Rs. (16000 + 200) = Rs. 16200

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107. Three Science classes A, B and C take a Life Science test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and C is 81. Then the average score of classes A, B and C is
     

1. 1. 81.5
      

   
   
   

   2. 81
      

   
   
   

   3. 80.5
      

   
   
   

   4. 80

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let Students in class A ⇒ p
   Students in class B ⇒ q
   Students in class C ⇒ r
   For classes A and B,
   

   83p + 76q	= 79
   p + q

   
   ⇒ 83p + 76q = 79p + 79q
   ⇒ 83p – 79p = 79q – 76q
   ⇒ 4p = 3q
   For classes B and C
   

   76q + 85r	= 81
   q + r

   
   ⇒ 76q + 85r = 81q + 81r
   ⇒ 5q = 4r
   ∴ 20p = 15q = 12r
   

   ⇒	20p	=	15q	=	12r
   	60		60		60

   
   

   ⇒	p	=	q	=	r
   	3		4		5

   
   

   Required average =	83 × 3 + 76 × 4 + 85 × 5
   	3 + 4 + 5

   
   

   Correct Option: A

   Let Students in class A ⇒ p
   Students in class B ⇒ q
   Students in class C ⇒ r
   For classes A and B,
   

   83p + 76q	= 79
   p + q

   
   ⇒ 83p + 76q = 79p + 79q
   ⇒ 83p – 79p = 79q – 76q
   ⇒ 4p = 3q
   For classes B and C
   

   76q + 85r	= 81
   q + r

   
   ⇒ 76q + 85r = 81q + 81r
   ⇒ 5q = 4r
   ∴ 20p = 15q = 12r
   

   ⇒	20p	=	15q	=	12r
   	60		60		60

   
   

   ⇒	p	=	q	=	r
   	3		4		5

   
   

   Required average =	83 × 3 + 76 × 4 + 85 × 5
   	3 + 4 + 5

   
   

   Required average =	249 + 304 + 425
   	12

   
   

   Required average =	978
   	12

   
   Required average = 81.5

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108. The average weight of first 11 persons among 12 persons is 95 kg. The weight of 12th person is 33 kg more than the average weight of all the 12 persons. The weight of the 12th person is
     

1. 1. 128.75 kg
      

   
   
   

   2. 128 kg
      

   
   
   

   3. 131 kg
      

   
   
   

   4. 97.45 kg

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let Weight of 12th person = w kg
   

   ∴ Average weight of 12 persons =		11 × 95 + w		kg
   		12

   
   According to the question,
   

   Correct Option: C

   Let Weight of 12th person = w kg
   

   ∴ Average weight of 12 persons =		11 × 95 + w		kg
   		12

   
   According to the question,
   

   ⇒ w =	11 × 95 + w	+ 33 = w
   	12

   
   ⇒ 1045 + w + 396 = 12w
   ⇒ 1441 = 11w
   ⇒ w =1441/11 = 131 kg.

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109. The average of 30 numbers is 40 and that of other 40 numbers is 30. The average of all the numbers is
     

1. 1. 34	2
      	7

      
      

   
   
   

   2. 35
      

   
   
   

   3. 34
      

   
   
   

   4. 34.5

   
   
   

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1. View Hint View Answer Discuss in Forum

   ∴ Average of all numbers =	30 × 40 + 40 × 30
   	70

   
   

   Average of all numbers =	240
   	7

   
   

   Average of all numbers = 34	2
   	7

   
   Second method to find the required average ,
   Here, n₁ = 30, a₁ = 40
   n₂ = 40, a₂ = 30
   

   ∴ Average =	n1a1 + n2a2
   	n1 + n2

   
   

   Correct Option: A

   ∴ Average of all numbers =	30 × 40 + 40 × 30
   	70

   
   

   Average of all numbers =	240
   	7

   
   

   Average of all numbers = 34	2
   	7

   
   Second method to find the required average ,
   Here, n₁ = 30, a₁ = 40
   n₂ = 40, a₂ = 30
   

   ∴ Average =	n1a1 + n2a2
   	n1 + n2

   
   

   ∴ Average =	30 × 40 + 40 × 30
   	70

   
   

   Average =	240
   	7

   
   

   Average = 34	2
   	7

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110. A library has an average number of 510 visitors on Sunday and 240 on other days. The average number of visitors per day in a month of 30 days beginning with Sunday is :
     

1. 1. 285
      

   
   
   

   2. 295
      

   
   
   

   3. 300
      

   
   
   

   4. 290

   
   
   

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1. View Hint View Answer Discuss in Forum

   That month will have 5 sundays.
   

   ∴ Required average =	5 × 510 + 25 × 240
   	40

   
   

   Required average =	2550 + 6000
   	30

   
   

   Required average =	8550	= 285
   	30

   
   Second method to find the required average ,
   Here,
   n₁ = 5, a₁ = 510
   n₂ = 25, a₂ = 240
   

   ∴ Average =	n1a1 + n2a2
   	n1 + n2

   
   

   Correct Option: A

   That month will have 5 sundays.
   

   ∴ Required average =	5 × 510 + 25 × 240
   	40

   
   

   Required average =	2550 + 6000
   	30

   
   

   Required average =	8550	= 285
   	30

   
   Second method to find the required average ,
   Here,
   n₁ = 5, a₁ = 510
   n₂ = 25, a₂ = 240
   

   ∴ Average =	n1a1 + n2a2
   	n1 + n2

   
   

   Average =	5 × 510 + 25 × 240
   	40

   
   

   Average =	2550 + 6000
   	30

   
   

   Average =	8550	= 285
   	30

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