311. The mean of 20 items is 55. If two items 45 and 30 are removed, the new mean of the remaining items is
     

1. 1. 65.1
      

   
   
   

   2. 65.3
      

   
   
   

   3. 56.9
      

   
   
   

   4. 56

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here , The mean of 20 items = 55.
   If two items 45 and 30 are removed, then
   Sum of 18 items = 55 × 20 – 45 – 30
   Sum of 18 items = 1100 – 75 = 1025
   

   Correct Option: C

   Here , The mean of 20 items = 55.
   If two items 45 and 30 are removed, then
   Sum of 18 items = 55 × 20 – 45 – 30
   Sum of 18 items = 1100 – 75 = 1025
   

   ∴ Required average =	1025
   	18

   
   Required average = 56.9

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312. The average weight of the 8 oarsmen in boat is increased by 1¹ /₂ kg when one of the crew who weighs 60 kg is replaced by a new man. The weight of the new man (in kg) is
     

1. 1. 70 kg
      

   
   
   

   2. 68 kg
      

   
   
   

   3. 71 kg
      

   
   
   

   4. 72 kg

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to question ,
   

   Weight of the new oarsman = 60 + 8 ×	3
   	2

   
   Weight of the new oarsman = 60 + 12 = 72 kg
   Second method to solve this question with the help of given formula :
   

   Here, N = 8, T = 60, t =	3
   	2

   
   Weight of new man = T + Nt
   

   Correct Option: D

   According to question ,
   

   Weight of the new oarsman = 60 + 8 ×	3
   	2

   
   Weight of the new oarsman = 60 + 12 = 72 kg
   Second method to solve this question with the help of given formula :
   

   Here, N = 8, T = 60, t =	3
   	2

   
   Weight of new man = T + Nt
   

   Weight of new man = 60 + 8 ×	3
   	2

   
   Weight of new man = 60 + 12 = 72

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313. There are 50 students in a class. One of them weighing 50 kg goes away and a new student joins. By this the average weight of the class increases by 1/2 kg. The weight of the new student is :
     

1. 1. 70 kg
      

   
   
   

   2. 72 kg
      

   
   
   

   3. 75 kg
      

   
   
   

   4. 76 kg

   
   
   

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1. View Hint View Answer Discuss in Forum

   Total weight increased =	1	× 50 = 25 kg
   	2

   
   ∴ Weight of the new man = Weight of the man + Total weight increased
   Weight of the new man = 50 + 25 = 75 kg.
   Second method to solve this question with the help of given formula :
   

   Here, N = 50, T = 50, t =	1
   	2

   
   Weight of New boy = T + Nt
   

   Correct Option: C

   Total weight increased =	1	× 50 = 25 kg
   	2

   
   ∴ Weight of the new man = Weight of the man + Total weight increased
   Weight of the new man = 50 + 25 = 75 kg.
   Second method to solve this question with the help of given formula :
   

   Here, N = 50, T = 50, t =	1
   	2

   
   Weight of New boy = T + Nt
   

   Weight of New boy = 50 + 50 ×	1	= 75 kg
   	2

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314. The average of seven numbers is 18. If one of the number is 17 and if it is replaced by 31, then the average becomes :
     

1. 1. 21.5
      

   
   
   

   2. 19.5
      

   
   
   

   3. 20
      

   
   
   

   4. 21

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given that , The average of seven numbers is 18.
   If one of the number is 17 and if it is replaced by 31 , then
   Difference = 31 – 17 = 14
   

   ∴ Required average = 18 +	14	= 20
   	7

   
   Second method to solve this question with the help of given formula :
   Here, n = 7, m = 18 , a = 31, b = 17
   

   New Average = m +	(a - b)
   	n

   
   

   Correct Option: C

   Given that , The average of seven numbers is 18.
   If one of the number is 17 and if it is replaced by 31 , then
   Difference = 31 – 17 = 14
   

   ∴ Required average = 18 +	14	= 20
   	7

   
   Second method to solve this question with the help of given formula :
   Here, n = 7, m = 18 , a = 31, b = 17
   

   New Average = m +	(a - b)
   	n

   
   

   New Average = m +	(31 - 17)
   	7

   
   

   New Average = 18 +	14
   	7

   
   New Average = 18 + 2 = 20

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315. The mean of 100 items was 46. Later on it was discovered that an item 16 was misread as 61 and another item 43 was misread as 34. It was also found that the number of items were 90 and not 100. Then what is the correct mean ?
     

1. 1. 50
      

   
   
   

   2. 50.7
      

   
   
   

   3. 52
      

   
   
   

   4. 52.7

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to question ,
   

   Required Average =	100 × 46 - 61 - 34 + 16 + 43
   	90

   
   

   Correct Option: B

   According to question ,
   

   Required Average =	100 × 46 - 61 - 34 + 16 + 43
   	90

   
   

   Required Average =	4600 - 36	=	4564
   	90		90

   
   Required Average = 50.7
   

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