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Average and Age Questions

81. There are four numbers - A, B, C and D. C is equal to 30% of average of A and B and D is 10% more than A. If ratio of A to B is 3 : 5 and sum of C and D is 180, then find average of all four numbers.




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Correct Ans:125
Explanation:
Given, C = 30% of (A + B)/2
---> C = (30/100) * (A + B)/2
---> C = (3/20) * (A + B) ----> eqn (i)

D = 10% of A + A
---> D = (10/100) * A + A
---> D = (1/10) * A + A
---> D = 11A/10 ----> eqn (ii)

A : B = 3 : 5
---> B = 5A/3 ----> eqn (iii)
Put value of eqn (iii) in eqn (i), to convert value of C interms of A only and to eliminate the paramater B
eqn (i) ---> C = (3/20) * (A + B)
---> C = (3/20) * (A + [5A/3])
---> C = (3/20) * (3A + 5A)/3
---> C = (1/20) * (8A)
---> C = 2A/5 ----> eqn (iv)

Given that, sum of C and D = 180
---> C + D = 180
Put values of eqn (iv) and eqn (ii) in the above eqn,
---> (2A/5) + (11A/10) = 180
---> (4A + 11A)/10 = 180
---> 15A/10 = 180
---> 3A/2 = 180
---> A = 180 * (2/3)
---> A = 120
From eqn (iii), B = 5A/3 = (5 * 120)/3 = 200
From eqn (iv), C = 2A/5 = 48
From eqn (ii), D = 11A/10 = 132

Required Average = (120 + 200 + 48 + 132) / 4 = 500/4 = 125
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82. Shalini"™s present age is five times of her daughter"™s present age and the ratio between Shalini"™s present age to her father"™s present age is 2 : 5. If the average age of all the three 6 years hence will be 43 years, then find the ratio of present ages of her daughter to the difference of the ages of Shalini and her father?




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Correct Ans:(2 :15)
Explanation:
Let daughter's present age be Z years.
Then, Shalini’s present age = 5Z years
---> Ratio of Shalini daughter's present age to Shalini’s present age = Z : 5Z = 1 : 5
Ratio of Shalini’s present age to her father’s present age = 2 : 5

Then, Ratio of present age of Daughter: Shalini : Father = 2 : 10 : 25
---> age of Daughter 6 years hence = 2x + 6
age of Shalini 6 years hence = 10x + 6
age of Father 6 years hence = 25x + 6

Given that, average age of all the three 6 years hence = 43 years
---> (2x + 6 + 10x + 6 + 25x + 6) / 3 = 43
---> (37x + 18) = 43 * 3
---> 37x = 129 - 18
---> 37x = 111
---> x = 111/37
---> x = 3
Then, present age of Daughter = 2x = 2 * 3 = 6 years
present age of Shalini = 10x = 10 * 3 = 30 years
present age of Father = 25x = 25 * 3 = 75 years

Required Ratio = 6 : (75 - 30)
= 6 : 45
= 2 : 15
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83. Sum of age of A & B is 12 years more than sum of age of B, C & D. Average age of C & D is 29 yrs. Find average age of A & D if D is 12 years elder than C.




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Correct Ans:52.5 yrs
Explanation:
Given that, Average of C & D = 29 years
---> (C + D) /2 = 29
---> C + D = 29 * 2 = 58 years ---> eqn (1)

Also given that, D is 12 years elder than C
---> D = C + 12
So eqn (1) becomes, C + C + 12 = 58
---> 2C = 58 - 12
---> 2C = 46
---> C = 23 years
and D = 23 + 12 = 35 years

Now, Sum of age of A & B is 12 years more than sum of age of B, C & D
---> A + B = 12 + B + C + D
---> A + B = 12 + B + 23 + 35
---> A = 70 years

Then, average age of A & D = (70 + 35) / 2
= 105/2
= 52.5 years
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84. Atif's age is 1/6th of his father's age. Atif's father Kayyum's age will be twice the age of Ravi's age after 10 years. If Ravi's tenth birthday was celebrated three years before, then what is Atif's present age.




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Correct Ans:6 years
Explanation:
Let present age of Ravi = r
Ravi's 10th birthday was three years ago
r = 10+3 = 13 years as x
Now, Ravi's age after 10 years
r + 10 = 13+ 10 = 23 years
Let present age of Atif and Kayyum be a and k respectively
k+10 = 2* (10+r)
k+10 = 2*(10+13)
k+10=20 +26
k = 46-10
k=36
Hence, age of Atif = k/6
=36/6
Age of Atif=6 years
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85. The sum of present ages of father and his son is 57 years. 6 years ago, the father was 4 times as old as his son at that time. The present age of son is:




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Correct Ans:15 years
Explanation:
Let son's present age = p years
Present age of father = (57 - p) years
(51-p-6) = 4(p-6)
51-p = 4p-24
p=15 years
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86. The average marks obtained by 50 students of a class is 92. If the 5 highest marks are removed, the average reduces by two mark. The average marks of the top 5 students is ________.




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Correct Ans:110
Explanation:
Average mark of 50 student is 92
Total marks = 92*50 = 4600
Its is given, that if 5 highest marks are removed, then the average mark reduces by 2
Therefore, Average of 42 = 90
Their sum is Sum of the removed 5 students is,
4600 - 4050=550
Their average is,
550/5=110
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87. If p, q, r be three positive numbers such that p > q > r when the smallest number is added to the difference of the rest two numbers, then the average of the resultant number and the original numbers except to the smallest number is 21 more than the average of all the three original numbers. The value of (p -q) is




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Correct Ans:63
Explanation:
From the given statement p > q > r ---> It is clear that P is the greatest number and r is the smallest number.
When the smallest number "r" is added to the difference of the rest two numbers "p and q", the resultant number becomes = r + (p - q)

Then, average of the resultant number and the original numbers except to the smallest number is 21 more than the average of all the three original numbers
---> [r + (p - q) + p + q] / 3 = 21 + [(p + q + r) / 3]
---> [(p - q) + p + q + r] / 3 = [63 + p + q + r] / 3
---> (p - q) + p + q + r = 63 + p + q + r
---> (p - q) = 63 + p + q + r - p - q - r
---> (p - q) = 63
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88. The average age of all the 100 employees in an office is 29 years, where (2/5) employees are ladies and the ratio of average age of men to women is 5 : 7. The average age of female employees is:




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Correct Ans:35 years
Explanation:
No. of employees = 100
Given, average age of all the 100 employees = 29 years
---> Total age of all the 100 employees = 29 * 100 = 2900

Total No. of female employees = (2/5) * 100 = 40
So, Total No. of Male employees = 100 - 40 = 60

Ratio of average age of men to women = 5 : 7
---> Average age of men = 5x
and, Average age of women = 7x

Now, Total age of male employees + Total age of female employees = Total age of all the 100 employees
---> (5x * 60) + (7x + 40) = 2900
---> 300x + 280x = 2900
----> 580x = 2900
----> x = 5
So, average age of female employees = 7x = 7 * 5 = 35 years
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89. The average age of Sachin and Ganguly is 35 years. If Kaif replaces Sachin, the average age becomes 32 years and if Kaif replaces Ganguly, then the average age becomes 38 years. If the average age of Dhoni and Irfan be half of the average age of Sachin, Ganguly and Kaif, then the average age of all the five people is 




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Correct Ans:28 years
Explanation:
Let the age of Sachin = S;
Ganguly = G;
Kaif = K;
Dhoni = D;
Irfan = I

Given that, Average age of Sachin and Ganguly = 35 years
---> (S + G)/ 2 = 35
Now, Total age of Sachin and Ganguly = 35 * 2
---> S + G = 70 ---> eqn (1)

Given that, If Kaif replaces Sachin, the avcrage age = 32 years
---> (K + G)/ 2 = 32
Now, Total age of Kaif and Ganguly = 32 * 2
---> K + G = 64 ---> eqn (2)

If Kaif replaces Ganguly, then the average age = 38 years
---> (S + K)/ 2 = 38
Now, Total age of Sachin and Kaif = 38 * 2
---> S + K = 76 ---> eqn (3)

Adding eqn (1), (2) and (3), we get
2S + 2G + 2K = 70 + 64 + 76
----> 2 (S + G + K) = 210
----> (S + G + K) = 210/2
----> (S + G + K) = 105

Given that, average age of Dhoni and Irfan = (1/2) * average age of Sachin, Ganguly and Kaif
---> (D + I)/2 = (1/2) * (S + G + K)/3
---> (D + I)/2 = (1/2) * (105/3)
---> (D + I)/2 = (1/2) * 35
---> (D + I) = (1/2) * 35 * 2
---> (D + I) = 35

Now, Average age of all the five people = (S + G + K + D + I)/5
= (105 + 35)/5
= 140/5
= 28 years
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90. The average age of a family of 6 members is 22 years. If the age of the youngest member be 7 years, whal was the average age of the family at the birth of the youngest member?




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Correct Ans:18 years
Explanation:
Given that, Total members in the family = 6
Average age of the family = 22 years

Total present age of the family of 6 members = 6 x 22 = 132 years

Given that, age of the youngest member = 7 years
Total age of the family of 6 members 7 years ago (ie.,) at
the birth of the youngest member = (132 - 7 * 6)
= 90 years

Therefore, at the birth of the youngest member, Total members in the family =5.
Average age of the family at the birth of the youngest member = 90 / 5
= 18 years
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91. The average weight of 40 students in a class is 75 kg. By mistake the weights of two students are read as 74 kg and 66 kg respectively instead of 66 kg and 54 kg. Find the corrected average weight of the class.




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Correct Ans:74.50 kg
Explanation:
Weight of 40 students = 40*75
New weight = 40*75 - 74-66 + 66 + 54
= 40*75 - 20
Therefore, the new average = (40*75-20)/40
= 74.50 kg
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92. Kaira is 4 years younger to his brother. Her father was 30 years old when her sister was born while her mother was 30 years old when she was born. If her sister was 4 years old when their brother was born, find the age of her father when her mother was born.




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Correct Ans:8
Explanation:
When Kaira was born, Mother was 30.
She is 4 years younger to her brother, so brother was 4 years old.
Sister was 4 years old when brother was born, so sister is 4 years elder to brother, so sister was 8 years old.
Father was 30 when sister was born, so father is 30 years elder to sister, so father was 30+8 = 38 years old.
Now when Kaira was born, mother was 30 and father was 38
So difference= 38-30 = 8 years.
So when mother was born, father was 8.
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93. At present, Ami's age is twice Rio's age and Cami is two years older than Ami. Two years ago, the respective ratio between Rio's age at that time and Cami's age at that time was 4 : 9. What will be Ami's age four years hence?




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Correct Ans:40 years
Explanation:
Let Rio's present age = x years
Then, Ami's present age = 2x years
Cami's present age = 2 + Ami's present age = (2+ 2x) years

Given, Two years ago, Rio's age : Cami's age = 4 : 9
---> (x - 2) / (2 + 2x - 2) = 4 / 9
---> (x - 2) / (2x) = 4 / 9
---> 9 * (x - 2) = 4 * (2x)
---> 9x - 18 = 8x
---> x = 18 ---> which is the present age of Rio

Then, Ami's age four years hence = Ami's present age + 4 years
= 2x + 4
= 2 * 18 + 4
= 36 + 4
= 40 years
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94. The average weight of 45 students in a class was calculated as 36 kg. It was later found that the weight of two students in the class was wrongly calculated. The actual weight of one of the boys in the class was 32 kg., but it was calculated as 34 kg., and the weight of another boy in the class was 45 kg.; whereas it was calculated as 40 kg. What is the actual average weight of the 45 students in the class? (Rounded off to two-digits after decimal)




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Correct Ans:36.07 kg
Explanation:
Actual weight of all the students = 36 * 45 - 34 + 32 - 40 + 45
= 1620 + 3
= 1623 kg

Actual average weight of the 45 students in the class = 1623 / 45
= 36.07 kg
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95. Shilpa"™s mother"™s age is five years more than twice the age of Shilpa. When Shilpa was born, her brother David was four years old and her father two years older than her mother. If the average age of her mother and father is 46 years. Find the ratio of age of David to that of Shilpa.




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Correct Ans:06:05
Explanation:
Let age of Shilpa = x, So age of Mother = 2x+5, David = x+4, Father = (2x+5)+2 = 2x+7
(2x+5 + 2x+7)/2 = 46
(4x+12) = 92
4x = 80
So, x = 20
So, (x+4)/x = 24/20 = 6/5
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96. Nithya is 4 years younger to his brother. Her father was 30 years old when her sister was born while her mother was was 30 years old when she was born. If her sister was 4 years old when their brother was born, find the age of her father when her mother was born.




SHOW ANSWER
Correct Ans:8
Explanation:
When Nithya was born:
Mother was 30 when Nithya born.
Nithya is 4 years younger to her brother, so when Nithya born her brother was 4 years old.
Her sister was 4 years old when brother was born, so sister is 4 years elder to brother, so sister was 8 years old when Nithya born.
Father was 30 when sister was born, so father is 30 years elder to sister, so father was 30+8 = 38 years old when Nithya born.
Now when Nithya was born, mother was 30 and father was 38
So difference in their ages is 8 years. So when mother was born, father was 8.
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97. The average of 3 consecutive natural numbers (which are in increasing order) is k. If two more consecutive numbers, just next to the first set of numbers, is added, then the new average becomes?




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Correct Ans:k+1
Explanation:
Given the average of 3 consecutive natural numbers in increasing order is K.
Let us assume,
3 consecutive natural numbers in increasing order be:
1,2,3
The average of these numbers = 1+2+3/3 = 2
Adding 2 more consecutive natural numbers,
1,2,3,4,5
The average of these numbers = 1+2+3+4+5/5 = 3
Again adding
1,2,3,4,5,6,7 two more consecutive natural numbers,
The average of these numbers = 1+2+3+4+5+6+7/5 = 4
So, it can be assumed that the average increases by 1.
So, the new average becomes = k+1
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98. The average of a batsman after 25 innings was 62 runs per innings. If after the 26th inning his average increased by 1 run, then what was his score in the 26th inning?




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Correct Ans:88
Explanation:
Runs in 26th inning = Runs total after 26 innings – Runs total after 25 innings
= [ 26 x ( 62+1) ] – [ 25 x 62 ]
= (26 x 63) – (25 x 62)
= 1638 – 1550 = 88
Hence, option (b) is the correct answer.
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99. A father said to his son,"I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, what was the son's age five years back?




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Correct Ans:14 years
Explanation:
Let son's present age be x years. Then,
38 - x = x
2x = 38
x = 19
Son's age 5 years back = 19 - 5 = 14 years.
Hence, option (c) is the correct answer.
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100. The average height of a group of 24 mens is 6 feet. If the height of the four mens be included, the average rises by 0.2 feet. The average height of the four mens was: 




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Correct Ans:7.4 feet
Explanation:
Let the average height of 4 mens be 'X'.
So, total height of 4 mens = 4X
Total height of 24 mens = 24*6 = 144 feet.

According to the question,
4X + 144 = 28(6 + 0.2)
4X + 144 = 168 + 5.6
4X = 173.6 - 144
4X = 29.6
X = 7.4 feet
Therefore, average height of 4 mens is 7.4 feet.
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