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Average and Age Questions

21. The ratio of present ages of Sri and Gowtham is 3: 4. Mahesh is 6 years older than Sri and two years younger than Gowtham. Find the sum of the present ages of Sri and Mahesh?




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Correct Ans:54 years
Explanation:
Given ratio of present ages of Sri and Gowtham = 3: 4
---> Present age of Sri = 3x
and Present age of Gowtham = 4x

Given, Mahesh is 6 years older than Sri and two years younger than Gowtham
---> Present age of Mahesh = Present ages of Sri + 6 = Present age of Gowtham - 2
---> Present age of Mahesh = 3x + 6 = 4x - 2
---> 3x + 6 = 4x - 2
---> 4x - 3x = 6 +2
---> x = 8
Therefore, Present age of Sri = 3x = 3 * 8 = 24 years
Present age of Mahesh = Present ages of Sri + 6 = 24 + 6 = 30 years

Now, Sum of the present ages of Sri and Mahesh = 24 + 30 = 54 years
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22. A library has an average of 510 visitors on Sundays and 240 on other days. What is the average number of visitors in a month of 30 days starting with sunday?




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Correct Ans:285
Explanation:
Given Total number of days in the month = 30
As the month begin with sunday, so there will be five sundays in the month.
Then, Number of days in the month excluding Sundays = 30 - 5 = 25

Now, Average number of visitors in the month = [(visitors on Sundays * no. of sundays) + (visitors on other days * no. of days excluding sundays)]/Total number of days in the month
= [(510 * 5) + (240 * 25)]/30
= [2550 + 6000]/30
= 8550/30
= 285
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23. Three years ago, Malini's age at that time was thrice of Rinu's age at that time. The respective ratio between Rinu's age six years hence and Malini's age eight years hence, will be 3 : 7. What will be Rinu's age two years hence? (in years)




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Correct Ans:20 years
Explanation:
Let the present ages of Malini be 'M' and 'Rinu' be R respectively.
3 years ago, the age of Malini was M - 3 and Rinu's age was R - 3
Given Three years ago, Malini's age at that time = 3* Rinu's age at that time
---> M - 3 = 3* (R - 3)
---> M - 3 = 3R - 9
---> M = 3R - 9 + 3
---> M = 3R - 6 ---> eqn (1)

Given, Rinu's age six years hence : Malini's age eight years hence = 3 : 7
---> (R + 6) : (M + 8) = 3 : 7
Substitute M = 3R - 6 from eqn (1) in the above eqn, we get
---> (R + 6) : (3R - 6 + 8) = 3 : 7
---> (R + 6)/(3R + 2) = 3/7
---> 7 * (R + 6) = 3 * (3R + 2)
---> 7R + 42 = 9R + 6
---> 9R - 7R = 42 - 6
---> 2R = 36
---> R = 18
Thus, present age of Rinu = R = 18 years
Now, Two years hence, Rinu's age = 18 + 2 = 20 years
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24. In a class, ratio of the number of boys to girls is 5:4 and the average weight of students in the whole class is 40 kg. Find the average weight of boys in the class if the average weight of girls in the class is 10 kg less than the average weight of students in the whole class.




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Correct Ans:48 kg
Explanation:
Given, ratio of Boys to Girls = 5 : 4
Let the number of Boys in the class = 5x
and number of Girls in the class = 4x
So, Total number of students = No. of Boys + No. of Girls = 5x + 4x = 9x

Given, average weight of students in the whole class = 40 kg
W.K.T: Average Weight = Total weight/Total number of persons
----> Total weight of all students/Total no. of students = 40
---> Total weight of all students/(5x + 4x) = 40
---> Total weight of all students/9x = 40
---> Total weight of all students = 360x

Given, average weight of girls in the class is 10 kg less than the average weight of students in the whole class
---> Average weight of girls = 40 kg - 10 kg = 30 kg
---> Total weight of girls/Total no. of girls = 30
---> Total weight of girls/4x = 30
---> Total weight of girls = 120x

Now, Total weight of all students = Total weight of Boys + Total weight of Girls
---> 360x = Total weight of Boys + 120x
---> Total weight of Boys = 360x - 120x = 240x

Hence, Average weight of boys in the class = Total weight of Boys/Total no. of Boys
= 240x/5x
= 48 kg
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25. If the two digits of Mr. Manoj's age are reversed, then the age obtained is the age of his wife. 1/11 of the sum of their ages is equal to the difference between their ages. If Mr. Manoj is older than his wife age, find the difference between his age.




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Correct Ans:9 years
Explanation:
Let the age of Mr Manoj be (10x + y) yrs.
∴ His wife's age = (x + 10y) years

Then, (10x + y + 10y + x) / 11 = 10x + y - 10y - x
(11x + 11y)/11 = 9x - 9y
x + y = 9x - 9y
8x = 10y
x/y = 5/4
So, x = 5 and y = 4
Manoj's age = (10*5) + 4 = 54 years
Manoj's wife's age = (10*4) + 5 = 45 years
Difference between their ages = 54 - 45 = 9 years
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26. There are five boxes in a cargo hold. The weight of the first box is 200 kg and the weight of the second box is 20% more than the weight of the third box, which is 25% more than the weight of the first box. The fourth box at 350 kg is 30% lighter than the fifth box. Find the difference in the average weight of the heaviest three and the lightest three.




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Correct Ans:133.33 kg
Explanation:
Weight of first box = 200 kg
According to question,
Weight of 2nd box = 250 * 6/5 = 300 kg
Weight of 3rd box = 200 * 5/4 = 250 kg
Weight of 4th box = 350 kg
Weight of 5th box = 350 * 10/7 = 500 kg
Average of 3 heaviest box = (500 + 350 + 300)/3 = 383.33 kg
Average of 3 lightest box = (200 + 250 + 300)/3 = 250 kg
Required answer = 383.33 - 250
= 133.33 kg
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27. The Ratio of ages of Mr. A and his wife are 4:3, and his son age"™s is 30% of the age of Mr. A. the age of his daughter is 50% more than that of his son. 5 years ago, the average age of his wife and daughter is 31 years. find out the difference between average age of his wife and daughter and that of Mr. A and his son.




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Correct Ans:3 yrs
Explanation:
Let ages of Mr. A. and his wife is 40x and 30x years respectively.
His son age = 30% of 40x = 12x
And his daughter age=50% more than that of his son
= (150/100)*12x =18x
His daughter and wife's present age
(wife - 5) + (daughter - 5) = 31*2
30x - 5 + 18x - 5 = 62
48x - 10 = 62
48x = 72
x = 3/2
So, age of his son = 12x = 18 years
His Daughter = 18x = 27 years
Mr. A. = 40x = 60 years
His wife = 30x = 45 years
so, (60 + 18)/2 - (27 + 45)/2 = 78/2 - 72/2
= 6/2 = 3 years
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28. The average weight of a class is decreased by 1, when 25 students joined the class, whose strength is 1/4th of the existing (or old) class and the total weight of the new students is 200 kgs. What is the new average weight of class?




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Correct Ans:12 kgs
Explanation:
The average weight of class = x
If the strength of old students = 100
The new students strength = 100 + 100*(1/4)
= 100 + 25 = 125
New students weight = 200 kgs
125(x - 1) = 100x + 200
125x - 125 = 100x + 200
125x - 100x = 200 + 125
25x = 325
x = 13
Required average = x - 1
= 13 - 1 = 12 kgs
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29. The sum of the present ages of a mother and her daughter is 60 years. Six years ago, mother's age was five times the age of the daughter. Find the daughter"™s age after 6 years.




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Correct Ans:20 yrs
Explanation:
Let the present ages of daughter and mother be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
⇒ 54 - x = 5x – 30
⇒ 6x = 84
⇒ x = 14.
⇒ Daughter's age after 6 years = (x+ 6) = 20 years.
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30. The present age of a father is 20 years less than three times his son"™s age. If the present age of the son, in years is an integer, which of the following choices represent the present age of the father?




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Correct Ans:55
Explanation:
Let the present ages of the father and the son be f and s respectively.
F = 3s - 20
s = (f + 20)/3
As s is an integer, so f + 20 is divisible by 3.
Going by the choices it must be 55 years.
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31. Present ages of Raj and Sudhan are in the ratio of 7 : 9 respectively. Five years ago ratio of their ages was 3 : 4. What will be Sudhan's age after 3 years from now?




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Correct Ans:48 years
Explanation:
Given:
Present ages of Raj and Sudhan = 7 : 9
5 yrs ago, ratio of their ages = 3 : 4
Let the present age of Raj and Sudhan be 7x and 9x respectively.
As per question,
(7x - 5)/(9x - 5) = 3/4
28x - 20 = 27x - 15
x = 5
So, present age of Sudhan = 9x = 9(5) = 45 yrs.
Sudhan's age after 3 yrs = 45 + 3 = 48 yrs.
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32. The average score of boys in an examination of a school is 71 and that of the girls is 73. The average score of the whole school in that examination is 71.8. Find the ratio of the number of boys to the number of girls that appeared in the examination.




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Correct Ans:3 : 2
Explanation:


Ratio of number of boys and number of girls = 1.2 : 0.8
= 12 : 8
= 3 : 2.
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33. The average age of a cricket team of 11 players is the same as it was 3 years back because 3 of the players whose current average age of 33 years were replaced by 3 youngsters. The average age of the newcomers is




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Correct Ans:22 years
Explanation:
Let average age of a cricket team of 11 players = X
Hence sum of ages of 11 players = 11X
3 years back the average was also X
Sum of ages was 11X
3 players had average age before 3 years = 30
Hence their total ages = 90
Total ages of remaining 8 players were 11X – 90
Now at present total ages of these 8 players
= (11X – 90) + 8*3 = 11X- 66
These 3 players were replaced by 3 younger players
Hence their sum of ages = 11X- (11X-66) = 66
Therefore average of their age= (66/3) = 22 years

Hence the answer is : 22 years
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34. Siva is 22 yrs younger than Uma. Siva's age is 72% of the sum of his and Uma's age. What will be Uma's age 15 yrs hence?




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Correct Ans:29
Explanation:
Given:
Siva's age = Uma's age + 22 ....(1)
Siva's age = 72%(Uma's age + Siva's age)
Siva's age = (72/100)Uma's age + (72/100)Siva's age
Siva's age - (72/100)Siva's age = (72/100)Uma's age
(28/100)Siva's age = (72/100)Uma's age
Siva's age = (18/7)Uma's age ....(2)

Sub (2) in (1),
(18/7)Uma's age = Uma's age + 22
(18/7)Uma's age - Uma's age = 22
(11/7)Uma's age = 22
Uma's age = 14 yrs
Uma's age 15 yrs hence = 14 + 15 = 29 yrs.
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35. Average weight of a class of boys is 24 kg. When a boy having weight 36 kg leaves the class and a new boy having weight 30 kg joins the class, then the average weight become 23.5 kg. How many boys are there in the class?




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Correct Ans:12
Explanation:
Let the number of boys in class be 'b'.
Average weight of a class of boys - 24 kg
So, weight of a class = 24b
New average weight of class = 23.5
So, weight of class = 23.5b

As per question,
Average weight of class - Weight of 36 kg boy leaves + Weight of 30 kg boy joins = New average weight of class
24b - 36 + 30 = 23.5b
24b - 23.5b = 6
0.5b = 6
b = 12
Therefore, number of boys in class = 12.
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36. The average temperature of Monday, Tuesday and Wednesday was 30° C and that of Tuesday, Wednesday and Thursday was 33° C. If the temperature on Monday was 32° C, then the temperature on Thursday was:




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Correct Ans:41° c
Explanation:
Let find the Temperature of Thursday:

----> Temperature of Monday, Tuesday and Wednesday = 30*3 = 90.
----> Temperature of Tuesday, Wednesday and Thursday 33*3 =99.
----> Thursday - Monday = 9
----> Thursday - 32 = 9
----> Thursday temperature = 32+9 = 41

Hence the answer is : 41 °
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37. The average revenues of 9 consecutive years of a company is Rs. 80 lakhs. If the average of first 5 years is Rs. 75 lakhs and that of last 5 years is Rs. 87 lakhs, find the revenue for the 5th year.




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Correct Ans:Rs. 90 lakhs
Explanation:
Given:
The average revenues of 9 consecutive years of a company = Rs 80 lakhs
Average of first 5 years = Rs 75 lakhs
Average of last 5 years = Rs 87 lakhs

Therefore, Revenue of 5th yr = Revenue of first 5 years + Revenue of last 5 years - Revenue of first 9 years
= (5 x 75) + (5 x 87) - (9 x 80)
= 90 lakhs.
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38. In a family of Father, daughter and son, age of father is twice the average age of whole family. Daughter"™s age is half the average age of the family. If son is 10 years old, what is the average age of the family?




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Correct Ans:20 yrs
Explanation:
Let the average age of family be X yrs.
Father's age = 2X
Daughter's age = X/2

[2X + (X/2) + 10]/3 = X
[4X + X + 20]/6 = X
[5X + 20]/6 = X
6X - 5x = 20
X = 20 yrs
Therefore, average age of family is 20 yrs.
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39. The average of twelve numbers is 42. The last five numbers have an average of 40 and the first four numbers have an average of 44. The sixth number is 6 less than the fifth number and 5 less than the seventh number. What will be the average of the 5th and 7th numbers?     




SHOW ANSWER
Correct Ans:44.5
Explanation:
Sum of twelve number = 12 * 42 = 504
Sum of last five numbers = 5 * 40 = 200
Sum of first four numbers = 4 *44 = 176
Sum of 5th, 6th and 7th numbers
----> 504 - (200 +176)
----> 504 - 376
----> 128

Let 5th, 6th and 7th numbers are (x+6), x and (x+5). Then,

-----> x+6+x+x+5 = 128
-----> 3x = 128 -11
-----> x = (117/3) = 39

Average of 5th and 7th number
-----> ((x+6+x+x+5)/2)
-----> = ((39+39+11)/2)
-----> = (89/2) = 44.5

Hence the answer is : 44.5
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40. In Santhosh opinion, his weight is greater than 54 kg but less than 63 kg. His brother does not agree with Santhosh and he thinks Santhosh's weight is greater than 50 kg but less than 60 kg. His father's view is that his weight cannot be greater than 57 kg. If all of them are correct in their estimation, what is the average of different portable weights of Santhosh?




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Correct Ans:56 kg
Explanation:
Let Santhosh's weight be y kg
According to Santhosh 54 < y < 63
According to Santhosh brother 50 < y < 60
According to Santhosh father y < 57
The value satisfying all the above conditions are 55, 56 and 57 Required average = 56 kg
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