The average of 11 numbers is 30. If the average of first six

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   The average of 11 numbers is 30. If the | Solutions

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5. The average of 11 numbers is 30. If the average of first six numbers is 17.5 and that of last six is 42.5, then what is the sixth number?

1. A. 30           👈Correct Answer
2. B. 36
3. C. 45
4. D. 50

1. Answer & Explanation:

   Sum of 11 Number is 11 x 30 = 330

   
   

   Given : 

   
   

    [ Avg of first 6 numbers is 17.5, so Sum of first Six Number is 6 x 17.5 ]
   
    [ Avg of Last 6 numbers is 42.5, so Sum of last Six Number is 6 x 42.5 ]
   
   6th Number :  ( Sum of first Six Number + Sum of last Six Number ) - 330
   
   Hence the 6th Number is 30

1. Related Question on The Average of:

1. The average marks scored by Ganesh in English, Science, Mathematics and History is less than 15 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography secured by him?

1. A. 40
2. B. 50
3. C. 60
4. D. Data inadequate

1. Answer : C ( 60 )

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1. The average weight of three men A, B and C is 84 kg. D joins them and the average weight of the four becomes 80 kg. If E, whose weight is 3 kg more than that of D, replaces A, the average weight of B, C, D and E becomes 79 kg. The weight of A is

1. A. 65 kg
2. B. 70 kg
3. C. 75 kg
4. D. 80 kg

1. Answer : C ( 75 kg )

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1. In a class of 100 students the average marks obtained by a student in Maths is 44. If we remove the highest and the lowest the average of the class becomes 43.92. A total of three students get either highest or lowest. What is the average of these three students?

1. A. 73.33
2. B. 46.66
3. C. 59.99
4. D. cannot be determined

1. Answer : B ( 46.66 )

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1. Find the average of first 20 natural numbers ?

1. A. 6
2. B. 7.5
3. C. 10.5
4. D. 12

1. Answer : C ( 10.5 )

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1. The average of 8 men is increased by 2 years when 2 of them whose ages are 21 and 23 years as replaced by two new men. The average age of two new men is 

1. A. 22 years
2. B. 24 years
3. C. 28 years
4. D. 30 years

1. Answer : D ( 30 years )

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1. The average age of a class is 15.8 years. The average age of the boys in the class is 16.4 years and that of the girls is 15.4 years. What is the ratio of boys to girls in the class ?

1. A. 2 : 3
2. B. 2 : 4
3. C. 3 : 4
4. D. 3 : 5

1. Answer : A ( 2 : 3 )

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1. The average weight of 8 men is increased by 1.5 Kg when one of the men who weights 65 Kg is replaced by a new man. The weight of the new man is

1. A. 65 Kg
2. B. 77 Kg
3. C. 82 Kg
4. D. 90 Kg

1. Answer : B ( 77 Kg )

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1. A hiker walked for two days. On the second day, the hiker walked 2 hrs. longer and at an average speed of 1 km per hour faster than he walked on the first day. If during the two days he walked a total of 64 km and spent a total of 18 hrs. walking, what was his average speed on the first day?

1. A. 2 km/h
2. B. 3 km/h
3. C. 4 km/h
4. D. 5 km/h

1. Answer : B ( 3 km/h )

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1. The average age of 8 persons in a committee is increased by 2 years when two men aged 35 years and 45 years are substituted by two women. The average age of these two women is

1. A. 41 years
2. B. 45 years
3. C. 48 years
4. D. 53 years

1. Answer : C ( 48 years )

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1. Of the four numbers whose average is 60, the first is one-fourth of the sum of the last three. The first number is

1. A. 15
2. B. 45
3. C. 48
4. D. 25

1. Answer : C ( 48 )

Problems on Average Questions with Solutions PDF

Basic Average Formula and Tricks

For Example : Find the average of all numbers between 5 and 49 which are divisible by 5. 

Solutions : Number are 5, 10, 15, 20, 25, 30, 35, 40, 45, These numbers are divided by 5.

Average Of numbers =	5+10+15+20+25+30+35+40+45	=	225
	9		9

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For Example : The average of 11 numbers is 30. If the average of first six numbers is 17.5 and that of last six is 42.5, then what is the sixth number? 

Solutions:   11 Number's Average is 30 [ Given ]

Sum of 11 Number's is 11 x 30 = 330

Average of first six numbers is 17.5 [ Given ] , so Sum of First 6 Number's is 17.5 x 6 = 105

Average of last six is 42.5 [ Given ] , so Sum of Last 6 Number's is 42.5 x 6 = 255

⇒ Sixth Number = ( Sum of First 6 Number's + Sum of Last 6 Number's ) - Sum of 11 Number's

⇒ Hence the Sixth Number is (105 + 255 ) - 330 = 30

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For Example : A person covers a distance of 50 km from P to Q at a speed of 30 km/hr and returns from Q to P at a speed of 40 km/hr. Find the average speed of person. 

Solutions:   Distance of 50 km from P to Q at a speed of 30 km/hr, Returns from Q to P at a speed of 40 km/hr 

Average Speed =	2 x 30 x 40	=	2400
	30 + 40		70

: : So the Average speed of the person = 34.28 km/hr

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  When new member is added or replaced by other member in the group.

 For Example : The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

Solutions:  Total weight increased = (8 x 2.5) kg = 20 kg.

Weight of new person = (65 + 20) kg = 85 kg.

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Average formula for n natural number = (n + 1) / 2

Average formula of n even numbers = (n + 1)

If number value increase or decrease by X, then the average also increase or decrease by A.

In AP ( Arithmetic Progression ), if number of terms are

i) Odd – Average is the middle term.

ii) Even – Average is the average of two middle terms.

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Objective Question On Average Problem

1. The average marks scored by Ganesh in English, Science, Mathematics and History is less than 15 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography secured by him?

1. A. 40     
2. B. 50      
3. C. 60        Correct Answer
4. D. Data inadequate      

2.  

   
   

   A Mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 72. If the marks secured by Beans were written as 36 instead of 86 then find the correct average marks up to two decimal places.

1. A. 73.41     
2. B. 74.3      
3. C. 72.43      
4. D. 73.43        Correct Answer

3.  

   
   

   The average age of a husband and wife was 23 when they were married 5 years ago. The average age of the husband, the wife and a child who was born dining the interval, is 20 years now. How old is the child now?

1. A. 9 months     
2. B. 1 year      
3. C. 3 years      
4. D. 4 years        Correct Answer

4.  

   
   

   The average of four consecutive even numbers is one-fourth of the sum of these numbers. What is the difference between the first and the last number?

1. A. 4     
2. B. 6        Correct Answer
3. C. 2      
4. D. Cannot be determined      

5.  

   
   

   Of the three numbers, the average of the first and the second is greater than the average of the second and the third by 15. What is the difference between the first and the third of the three numbers

1. A. 15       Correct Answer
2. B. 45      
3. C. 60      
4. D. None of these      

6.  

   
   

   The average of 25 results is 18, that of first 12 is 14 and of the last 12 is 17 Thirteenth result is

1. A. 72     
2. B. 78        Correct Answer
3. C. 85      
4. D. 28      

7.  

   
   

   Average age of seven persons in a group is 30 years. The average age of five persons of this group is 31 years.  What is the average age of the other two persons in the group?

1. A. 55 years       Correct Answer
2. B. 26 years      
3. C. 15 years      
4. D. None of these      

8.  

   
   

   Average weight of three boys P, T and R is 54(1/3) kg while the average weight of three boys T, F and G is 53 kg. What is the average weight of P, T, R, F and H

1. A. 53.8 kg     
2. B. 52.4 kg      
3. C. 53.2 kg      
4. D. Data inadequate         Correct Answer

9.  

   
   

   In a class of 52 students the number of boys is two less than the number of girls. Average weight of the boys is 42 kg, while the average weight of all the 52 students is 40 kg. Approximately what is the average weight of the girls?

1. A. 41 kg     
2. B. 29 kg      
3. C. 40 kg      
4. D. 38 Kg        Correct Answer

10.  

    
    

    While calculating the average of a batsman as 36 in 100 matches that he played, one of the score 90 was incorrectly noted as 40. The percentage error is

1. A. 0.6%     
2. B. 1.36%        Correct Answer
3. C. 1.34%      
4. D. 121%       

11.  

    
    

    The average sale of a car dealership was 15 cars per week. After a promotional scheme, the average sale increased to 21 car per week. The percentage increase in the sale of Car was 

1. A. 40%        Correct Answer
2. B. 140%       
3. C. 42(6/7)%      
4. D. 39.33%      

12.  

    
    

    In a class with a certain number of students, if one new student weighing 50 kg is added, then the average weight of the class increased by 1 kg. If one more student weighing 50 kg is added, then the average weight of the class increases by 1.5 kg over the original average. What is the original weight (in kg) of the class?

1. A. 46      
2. B. 42      
3. C. 27      
4. D. 47        Correct Answer

13.  

    
    

    The average marks of a student in 8 subjects are 87. Of these, the highest marks are 2 more than the one next in value. If these two subjects are eliminated, the average mark of the remaining subjects is 85. What is the highest mark obtained by him?

1. A. 94       Correct Answer
2. B. 91      
3. C. 89      
4. D. 96