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Average and Age Questions

1. Find the average of the first 70 natural numbers



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Correct Ans:35.5
Explanation:
Solution is
Average of n natural numbers = (n + 1 ) / 2
= ( 70 + 1 ) / 2
= 71 / 2
= 35.5
Answer is 35.5


2. The average weight of a class having 14 students is 44 kg. Find the total weight of the class.



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Correct Ans:616
Explanation:
Solution is
Average = Total Quantity / No. of Quantity
Total quantity = Avg x No. of Quantity

Total quantity = 14 x 44
= 616
Answer is 616


3. Find the average of the first 27 natural numbers



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Correct Ans:14
Explanation:
Solution is
Average of n natural numbers =( n + 1 ) / 2
Average of 27 natural numbers = ( 27 + 1 ) / 2
= 28 / 2
= 14
Answer is14


4. The average weight of 16 students in a class is 36 kg. Find the total weight of the class.



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Correct Ans:576
Explanation:
Average = Total Quantity / No. of Quantity Total quantity = Avg x No. of Quantity Total quantity = 16 x 36 = 576


5. Find the average of the first 27 natural numbers



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Correct Ans:14
Explanation:
Solution is
Average of n natural numbers =( n + 1 ) / 2
Average of 27 natural numbers = ( 27 + 1 ) / 2
= 28 / 2
= 14
Answer is14


6. The average weight of a class having 16 students is 36 kg. Find the total weight of the class.



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Correct Ans:576
Explanation:
Solution is
Given :
Average weight of a class having 16 students is 36 kg
Average = Total Quantity / No. of Quantity
Total quantity = Avg x No. of Quantity

Total quantity = 16 x 36 = 576
Answer is 576


7. Find the average of first 17 multiples of 3 



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Correct Ans:27
Explanation:
Solution is
Given

Average of first 17 natural numbers=(n + 1 ) / 2
= ( 18 / 2)
= 9
Average of first 17 multiples of 3 =(Average of first 17 natural numbers) x 3
= 9 * 3
= 27.


8. Find the average of the first 56 natural numbers 



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Correct Ans:28.5
Explanation:
Solution is
Average of n natural numbers = (n + 1) / 2
= (56 + 1) / 2
= 57 / 2
= 28.5
Answer is 28.5


9. The average weight of 16 class having a students is 36 kg. Find the total weight of the class.



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Correct Ans:576
Explanation:
Average = Total Quantity / No. of Quantity Total quantity = Avg x No. of Quantity Total quantity = 16 x 36 = 576


10. Find the average of first 17 multiples of 3



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Correct Ans:27
Explanation:
The multiples of 3 are : 3,6,9,...,51 Average = (3+6+9+...51)/17 Average = 27


11. Find the average of the first 56 natural numbers.



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Correct Ans:28.5
Explanation:
Average = (1+2+...+56)/56
= (56*57)/(2*56)
= 57/2

Average = 28.5


12. There were 45 students in a hostel, if the number of students increased by 7, the expenses of the mess were increased by Rs. 39 per day while the average expenditure per head diminished by Re.1. What is the original expenditure of the mess (in Rs)? 



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Correct Ans:585
Explanation:
Let the original expenditure be Rs.x
Original average expenditure = X/45
New average expenditure = (x+39)/52

So (x/45) - ((x+39) / 52) = 1
=> x = 585
so, original expenditure is Rs 585


13. The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 65 kg. What is the correct weight?



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Correct Ans:58.85
Explanation:
Actual total weight is (20X 58.4 - 56 + 65) = 1177 Kgs Actual average weight is 1177/20 = 58.85kgs


14. Average of 13 results is 65. If the average of first six results is 61 and average of last six results is 59. Then find the seventh result? 



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Correct Ans:125
Explanation:
Total = 13 x 65 = 845
Total of first six = 366 and total for last six = 354
Seventh result = total ? (total of first six + total for last six)
= 845 - ( 366 + 354 )
= 125


15. If the average income of a family of 'x' members is Rs. 25000 while average income of another family of 6 members is Rs. 32000, then find the value of 'x' if the average income of both families is Rs. 28000 



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Correct Ans:8
Explanation:
Avg income of 1st family=25
Avg income of 2nd family=32
Both the families=28
1st family=28-25=3
2nd family=32-28=4
Requied ratio=4:3
Ratio of number of family members of 1stto 2ndis 4 : 3.
In the second family, there are 6 members,
Hence in the 1stfamily there are 8 members, only then the ratio
= 8 : 6 or 4 : 3
Hence x = 8.


16. Find the average of first 26 multiples of 11



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Correct Ans:148.5
Explanation:
Solution is:
The multiples of 11 are : 11,22,33,...,286 Average = (11+22+33+...286)/26 Average = 148.5


17. Find the sum of first 15 odd natural numbers.



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Correct Ans:225
Explanation:
Sum of first n odd natural numbers = n2

Sum of first 15 odd natural numbers = 152 = 225


18. Find the average of the following set of score: 188, 128, 155, 168, 199, 178, 145, 168 



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Correct Ans:166.13
Explanation:
188 + 128 + 155 + 168 + 199 + 178 + 145 + 168
= 1329 / 8
= 166.125
Approx, 166.13


19. The average weight of 8 persons increases by 1.5kg when a person weighing 65kg is replaced by a new person. What could be the weight of the new person?



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Correct Ans:77
Explanation:
Let the average weight of 8 persons be 'x' kg and
the weight of the new person be 'y' kg

Given,average weight of 8 persons increases by 1.5kg
so, (8x - 65 + y) / 8 = x + 1.5
=> 8x - 65 + y = 8x + 12
=> 8x - 8x + y = 12 + 65
=> y = 77

Thus, the weight of the new
person be y = 77 kg


20. The average of 12 numbers is 24. If each number be multiplied by 6. Find the average of new set of numbers?



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Correct Ans:144
Explanation:
New Average = Old Average x 6 = 24 x 6 = 144



1...1...89


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