# Average and Age Questions and Answers updated daily – Aptitude

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## Average and Age Questions

101. The average age of Sai's family consisting of 4 members, 4 years ago, was 28 years. 2 years ago, a baby was born in the family. The average age of the family 2 years from now would be :

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Correct Ans:28 years

Explanation:

4 years ago, total age of 4 members = 4 x 28 = 112 years

Present age of 4 members = 112+(4 x 4) = 128 years

New born baby present age = 2 years

So, present age of 5 members = 128 + 2 = 130 years

2 years hence the total age of the family = 130 + (5 x 2) = 140 years

Average age of the family two years hence = 140 / 5 = 28 years

Present age of 4 members = 112+(4 x 4) = 128 years

New born baby present age = 2 years

So, present age of 5 members = 128 + 2 = 130 years

2 years hence the total age of the family = 130 + (5 x 2) = 140 years

Average age of the family two years hence = 140 / 5 = 28 years

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102. Krish, Harish and Dinesh are three Brothers. Krish and Harish are twins. The ratio of sum of the ages of Krish and Harish is same as that of Dinesh alone. Three years earlier the ratio of age of Krish and Dinesh was 5 : 11. What will be the age of Dinesh 7 years hence?

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Correct Ans:None of these

Explanation:

Since Krish and Harish are twins so their ages be same.

Let their ages be x and and age of Dinesh be y,

then, x + x = y y = 2x .........(i)

and (x – 3)/(y – 3) = 5/11

⇒ 11x – 33 = 5y – 15

⇒ 11x – 5y = 18 ...........(ii)

Sub equ(i) in equ(ii),we get

11x – 10x = 18

⇒ x = 18

So, the age of Dinesh 7 years hence will be

18 + 18 + 7 = 43 years.

Hence, option E is correct.

Let their ages be x and and age of Dinesh be y,

then, x + x = y y = 2x .........(i)

and (x – 3)/(y – 3) = 5/11

⇒ 11x – 33 = 5y – 15

⇒ 11x – 5y = 18 ...........(ii)

Sub equ(i) in equ(ii),we get

11x – 10x = 18

⇒ x = 18

So, the age of Dinesh 7 years hence will be

18 + 18 + 7 = 43 years.

Hence, option E is correct.

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103. The average height of 40 pencils is 154 cm. Some pencils of average height 160 cm are taken out. If the new average height is 150 cm, then how many pencils are remaining?

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Correct Ans:24

Explanation:

Let number of pencils taken out be

Total number of pencils = 40

Average height of 40 pencils = 154 cm

Average height of taken out pencils = 160 cm.

As per question,

Total height of 40 pencils - Total height of pencils that taken out = Total height of remaining pencils

(40 x 154) - 160X = 150(40 - X)

6160 - 160X = 6000 - 150X

160 = 10X

X = 16

**'X'.**Total number of pencils = 40

Average height of 40 pencils = 154 cm

Average height of taken out pencils = 160 cm.

As per question,

Total height of 40 pencils - Total height of pencils that taken out = Total height of remaining pencils

(40 x 154) - 160X = 150(40 - X)

6160 - 160X = 6000 - 150X

160 = 10X

X = 16

**Remaining pencils**= 40 - X = 40 - 16 =**24.**
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104. If Ram is one-third the age of his father Raj now, and was one-fourth the age of his father 5 years ago, then how old will his father Raj be 5 years from now?

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Correct Ans:50 years

Explanation:

Let the present age of Ram be

At present, Ram is one-third the age of his father Raj.

So, present age of father = 3x

According to the question,

3x - 5 = 4(x - 5)

3x - 5 = 4x - 20

x = 15 years

Therefore, present age of father = 3x = 3(15) = 45 years

So, father's age after 5 years = 45 + 5 =

**'x'.**At present, Ram is one-third the age of his father Raj.

So, present age of father = 3x

According to the question,

3x - 5 = 4(x - 5)

3x - 5 = 4x - 20

x = 15 years

Therefore, present age of father = 3x = 3(15) = 45 years

So, father's age after 5 years = 45 + 5 =

**50 years.**
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105. Mr. A and Mrs. B have two sons P and Q and a daughter R. R is the youngest among the three children. Mrs. B is five years younger than Mr. A. The ages of the children form an Arithmetic Progression whose common difference is 1. The sum of the ages of the male members is 92 while that of the female members of the family is 67. What is the sum of the ages of Mr. A and Mrs. B?

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Correct Ans:105

Explanation:

Given, ages of the children form an Arithmetic Progression whose common difference is 1.

So, let the age of children be

Here, a-1 is the youngest child who is the daughter R.

B is 5 yrs younger than A,

A = B + 5

Sum of ages of female members = 67.

a-1 + B = 67

Sum of ages of female members = 91

a + a+1 + A = 91

2a + A = 91

2a + (B + 5) = 91

Solving equations (i) and (ii),

a = 18; B = 50

Therefore, A = B + 5 = 50 + 5 = 55 yrs

Sum of the ages of Mr. A and Mrs. B = 55 + 50 =

So, let the age of children be

**a-1, a, a+1.**Here, a-1 is the youngest child who is the daughter R.

B is 5 yrs younger than A,

A = B + 5

Sum of ages of female members = 67.

a-1 + B = 67

**a + B = 68**...(i)Sum of ages of female members = 91

a + a+1 + A = 91

2a + A = 91

2a + (B + 5) = 91

**2a + B = 86**....(ii)Solving equations (i) and (ii),

a = 18; B = 50

Therefore, A = B + 5 = 50 + 5 = 55 yrs

Sum of the ages of Mr. A and Mrs. B = 55 + 50 =

**105 yrs.**
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106. There are three groups A, B and C. The average of group A is 93. The average of group B is 86. The average of group C is 95. The average of group A and B is 89, the average of group B and C is 91. Find the average of the three groups?

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Correct Ans:91.5

Explanation:

By alligation method,

Ratio of A : B : C = 3 : 4 : 5

Average of all 3 groups = [(93 x 3) + (86 x 4) + (95 x 5)]/(3 + 4 + 5)

= (279 + 344 + 475)/12

= 1098/12

= 91.5

Therefore,

Ratio of A : B : C = 3 : 4 : 5

Average of all 3 groups = [(93 x 3) + (86 x 4) + (95 x 5)]/(3 + 4 + 5)

= (279 + 344 + 475)/12

= 1098/12

= 91.5

Therefore,

**average of all three groups = 91.5.**
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107. Sobha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?

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Correct Ans:6 years

Explanation:

Let the Shoba's age be

Shoba's brother's age = x - 4

Shobha's father's age = x + 38

Shobha's mother's age = 36 + (x - 4) = 32 + x

Difference between Shobha's father and mother = (x + 38) - (32 + x)

= x + 38 - 32 - x

=

**'x'**.Shoba's brother's age = x - 4

Shobha's father's age = x + 38

Shobha's mother's age = 36 + (x - 4) = 32 + x

Difference between Shobha's father and mother = (x + 38) - (32 + x)

= x + 38 - 32 - x

=

**6 years.**
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108. Udit is 8 years older than his brother. His brother is 24 years younger than their mother. If the ratio between the ages of Udit and their mother is 7 : 11. What will be the age of Udit’s brother after 3 years?

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Correct Ans:23

Explanation:

Let the age of Udit's brother be

Udit age = a + 8

Mother's age = a + 24

Given, the ratio between the ages of Udit and their mother is 7 : 11.

(a + 8)/(a + 24) = 7/11

(a + 8)11 = (a + 24)7

11a + 88 = 7a + 168

11a - 7a = 168 - 88

4a = 80

a = 20

Hence, Udit's brother present age = 20 yrs

Therefore, Udit's brother age after 3 years = 20 + 3 =

**'a'.**Udit age = a + 8

Mother's age = a + 24

Given, the ratio between the ages of Udit and their mother is 7 : 11.

(a + 8)/(a + 24) = 7/11

(a + 8)11 = (a + 24)7

11a + 88 = 7a + 168

11a - 7a = 168 - 88

4a = 80

a = 20

Hence, Udit's brother present age = 20 yrs

Therefore, Udit's brother age after 3 years = 20 + 3 =

**23 yrs.**
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109. The average weight of 17 boxes is 92 kg. If 18 new boxes are added, the new average increases by 3 kg. What will be the average weight of the 18 new boxes?

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Correct Ans:97.8 kg

Explanation:

Given that, average weight of 17 boxes = 92 kg

So, weight of 17 boxes = 17 x 92 = 1564 kg

If 18 boxes are added, the average weight increases by 3 kg

Therefore, total number of boxes= 17 + 18 boxes = 35 boxes

Total weight of 35 boxes = 35 x (92 + 3) = 3325 kg

Therefore, weight of 18 boxes = 3325 - 1564 = 1761 kg

Thus, average weight of 18 boxes = 1761/18 =

So, weight of 17 boxes = 17 x 92 = 1564 kg

If 18 boxes are added, the average weight increases by 3 kg

Therefore, total number of boxes= 17 + 18 boxes = 35 boxes

Total weight of 35 boxes = 35 x (92 + 3) = 3325 kg

Therefore, weight of 18 boxes = 3325 - 1564 = 1761 kg

Thus, average weight of 18 boxes = 1761/18 =

**97.8 kg.**
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110. 1 year ago, a mother was 4 times older to her son. After 6 years, her age becomes more than double her son’s age by 5 years. The ratio of present age of mother to the present age of son will be:

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Correct Ans:25:7

Explanation:

Let the present age of mother be x and present age of son be y.

Given, 1 yr ago mother's age = 4 times of son's age

x - 1 = 4(y - 1)

x - 1 = 4y - 4

x = 4y - 3

And also given, after 6 yrs mother's age = double the son's age by five yrs

x + 6 = 2(y + 6) + 5

(4y - 3) + 6 = 2y + 12 + 5

4y + 3 = 2y + 17

4y - 2y = 17 - 3

2y = 14

y = 7 yrs

Therefore, mother's age = 4(7) - 3 = 28 - 3 = 25 yrs

Required ratio of present age of mother and son = 25 : 7.

Given, 1 yr ago mother's age = 4 times of son's age

x - 1 = 4(y - 1)

x - 1 = 4y - 4

x = 4y - 3

And also given, after 6 yrs mother's age = double the son's age by five yrs

x + 6 = 2(y + 6) + 5

(4y - 3) + 6 = 2y + 12 + 5

4y + 3 = 2y + 17

4y - 2y = 17 - 3

2y = 14

y = 7 yrs

Therefore, mother's age = 4(7) - 3 = 28 - 3 = 25 yrs

Required ratio of present age of mother and son = 25 : 7.

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111. There are 25 students in a class and the average of their ages is 15 years. The average age of the first 12 students is 14 and the average age of the last 12 students is 16. If the age of Amrutha is 5 years more than the age of 13th student, find the age of Amrutha.

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Correct Ans:20

Explanation:

Given, average age of 25 students = 15 yrs

WKT,

Total age of 25 students = 15 x 25 = 375 yrs

Average age of first 12 students = 14 yrs

So, the total age of first 12 students = 14 x 12 = 168 yrs

Average age of last 12 students = 16 yrs

So, total age of last 12 students = 12 x 16 = 192 yrs

Therefore, age of 13th student = Total age of 25 students - (Total age of first 12 students + Total age of last 12 students)

Age of 13th student = 375 - (168 + 192) = 15 yrs

Age of Amrutha = 5 + age of 13th student = 5 + 15

Amrutha's age = 20 yrs.

WKT,

**Average age = Total age/Number of students**Total age of 25 students = 15 x 25 = 375 yrs

Average age of first 12 students = 14 yrs

So, the total age of first 12 students = 14 x 12 = 168 yrs

Average age of last 12 students = 16 yrs

So, total age of last 12 students = 12 x 16 = 192 yrs

Therefore, age of 13th student = Total age of 25 students - (Total age of first 12 students + Total age of last 12 students)

Age of 13th student = 375 - (168 + 192) = 15 yrs

Age of Amrutha = 5 + age of 13th student = 5 + 15

Amrutha's age = 20 yrs.

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112. The average age of 33 students and the class teacher in a class is 15 years. If the class teacher's age is 48 years. What would be the average age of only the students?

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Correct Ans:14 years

Explanation:

Given:

Average age of 33 students and a teacher = 15 yrs

Age of teacher = 48 yrs

Total age of all students = (15*34) - 48

= 510 - 48

= 462 yrs

Required average age = 462/33 =14 yrs

Therefore, average age of students = 14yrs.

Average age of 33 students and a teacher = 15 yrs

Age of teacher = 48 yrs

Total age of all students = (15*34) - 48

= 510 - 48

= 462 yrs

Required average age = 462/33 =14 yrs

Therefore, average age of students = 14yrs.

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113. A student bought 6 books namely A, B, C, D, E and F at Rs.111, Rs.95, Rs.50, Rs.125, Rs.75 and Rs.x respectively. If the average of all these books is Rs.6 more than the average cost of books B, C and D, find the value of x.

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Correct Ans:120

Explanation:

According to the question,

Average of 6 books = Average of B, C and D + 6

[(111 + 95 + 50 + 125 + 75 + x)/6] = [(95 + 50 + 125)/3] + 6

(456 + x)/6 = (270/3) + 6

(456 + x)/6 = 96

456 + x = 576

x = 576 - 456

x = 120

Therefore, the value of x is 120.

Average of 6 books = Average of B, C and D + 6

[(111 + 95 + 50 + 125 + 75 + x)/6] = [(95 + 50 + 125)/3] + 6

(456 + x)/6 = (270/3) + 6

(456 + x)/6 = 96

456 + x = 576

x = 576 - 456

x = 120

Therefore, the value of x is 120.

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114. The average of 9 integers is found to be 11. But after the calculation, it was detected that, by mistake, the integer 23 was copied as 32, while calculating the average. After the due correction is made, the new average will be

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Correct Ans:10

Explanation:

Difference of numbers = 23 - 32

= -9

There are 9 integers

So, the average of -9 = -9 / 9 = -1

The new average = 11 - 1 = 10

= -9

There are 9 integers

So, the average of -9 = -9 / 9 = -1

The new average = 11 - 1 = 10

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115. B was born when A was 4 years 7 month and C was born when B was 3 years 4 months old. When C was 5 years 2 months old, then their average age was

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Correct Ans:8 years 11 months

Explanation:

By question, we should calculate from Câ€™s age

Given that,

C = 5 years 2 months

From the age of C, the age of B can be written as

B = (5 + 3) years (2 + 4) months

= 8 years 6 months

From the age of B, the age of A can be written as

A = (8 + 4) years (6 + 7) months

= 12 years 13 months

(12 months become 1 year)

A = 13 years 1 month

Average = (A + B + C)/3

= (8 + 5 + 13) years (6 + 2 + 1) months/3

= (26 years 9 months)/3

(balance 2 years become 24 months

So, 24 + 9 = 33)

= 8 years 11 months

Therefore, average = 8 years 11 months

Given that,

C = 5 years 2 months

From the age of C, the age of B can be written as

B = (5 + 3) years (2 + 4) months

= 8 years 6 months

From the age of B, the age of A can be written as

A = (8 + 4) years (6 + 7) months

= 12 years 13 months

(12 months become 1 year)

A = 13 years 1 month

Average = (A + B + C)/3

= (8 + 5 + 13) years (6 + 2 + 1) months/3

= (26 years 9 months)/3

(balance 2 years become 24 months

So, 24 + 9 = 33)

= 8 years 11 months

Therefore, average = 8 years 11 months

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116. The average salary of all staff of a school is Rs. 10,000. The average salary of 20 teaching staff is Rs. 12,000 and that of non-teaching staff is Rs.5000, the number of non-teaching staff will be

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Correct Ans:8

Explanation:

Let number of non-teaching staff be x.

Average salary of all staff = Rs. 10,000

Average salary of 20 teaching staff = Rs. 12,000

Average salary of non-teaching staff = Rs.5000

Since, Average salary of teaching staff + Average salary of no-teaching staff = Average salary of all staff

(20*12000) + (x*5000) = (x + 20)*10000

240000 + 5000x = (x + 20)*10000

Divide the equation 1000,

240 + 5x = (x + 20)*10

240 + 5x = 10x + 200

10x - 5x = 240 - 200

5x = 40

x = 8

Average salary of all staff = Rs. 10,000

Average salary of 20 teaching staff = Rs. 12,000

Average salary of non-teaching staff = Rs.5000

Since, Average salary of teaching staff + Average salary of no-teaching staff = Average salary of all staff

(20*12000) + (x*5000) = (x + 20)*10000

240000 + 5000x = (x + 20)*10000

Divide the equation 1000,

240 + 5x = (x + 20)*10

240 + 5x = 10x + 200

10x - 5x = 240 - 200

5x = 40

x = 8

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117. The present age of a father is 3 yr more than three times the age of his son. 3 yr hence, father's age will be 10 yr more than twice the age of the son. The father's present age is

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Correct Ans:33 yr

Explanation:

Let the son's present age be x yr.

Given that, father's age is 3 yr more than three times the age of his son.

Father's age = 3x + 3

Accoroding to the question, after 3 yr

Father's age = 10 yr more than twice the age of the son

(3x + 3) + 3 = 2(x + 3) + 10

3x + 6 = 2x + 6 + 10

3x + 6 = 2x + 16

3x - 2x = 16 - 6

x = 10

Therefore, father's present age = 3x + 3 = 3(10) + 3 = 33 yr.

Given that, father's age is 3 yr more than three times the age of his son.

Father's age = 3x + 3

Accoroding to the question, after 3 yr

Father's age = 10 yr more than twice the age of the son

(3x + 3) + 3 = 2(x + 3) + 10

3x + 6 = 2x + 6 + 10

3x + 6 = 2x + 16

3x - 2x = 16 - 6

x = 10

Therefore, father's present age = 3x + 3 = 3(10) + 3 = 33 yr.

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118. 3 yr ago, the average of a family of 5 members was 17 yr. A baby having been born, the average age of the family is same today. the present age of the baby is

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Correct Ans:2 yr

Explanation:

Present age of family of 5 members = (17*5) + (5*3)

= 85 + 15 = 100 years

Given, average age of family is same 17 yrs.

Total age of family of 6 members(including baby) = 6*17 = 102 years

Therefore, present age of baby = 102 - 100 = 2 yr.

= 85 + 15 = 100 years

Given, average age of family is same 17 yrs.

Total age of family of 6 members(including baby) = 6*17 = 102 years

Therefore, present age of baby = 102 - 100 = 2 yr.

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119. Present age of A is 3 years less than present age of B. Ratio of B"™s age 5 year ago and A"™s age 4 year hence is 3 : 4 then find present age (in years) of A.

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Correct Ans:20

Explanation:

Let Bâ€™s age = ð‘¥

So Aâ€™s age = ð‘¥ âˆ’ 3

x-5/x+1= 34

ð‘¥ = 23

Aâ€™s age = 23âˆ’3 = 20 years

So Aâ€™s age = ð‘¥ âˆ’ 3

x-5/x+1= 34

ð‘¥ = 23

Aâ€™s age = 23âˆ’3 = 20 years

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120. When the couple was married the average of their ages was 25 years. When their first child was born, the average age of family became 18 years. When their second child was born, the average age of the family became 15 years. Find the average age of the couple now.

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Correct Ans:29

Explanation:

Average ages of couple = 25 years

So, the sum of ages of couple = 25*2 = 50 years

When 1st child born the average age of family = 18 years

Therefore, the total age of family(3 members) = 18 * 3 = 54 years

(At that time child age would be zero, so the age of father and mother would have increased by same.)

Its increased by 2 years for each = 50 + 2 + 2 = 54 years

When second child born the average age of family = 15 years

Therefore, the total age of family(4 members) = 15 * 4 = 60 years

(So, at that time second child age would be zero, the age of father, mother and first child would have increased by same.)

So its increased by 2 years for each = 54 + 2 + 2 + 2 = 60 years.

Therefore after 4 years, the total age of couple (from age of 50) = 50 + 4 + 4 = 58 years

So, the average age of couple = 58/2 = 29 years.

So, the sum of ages of couple = 25*2 = 50 years

When 1st child born the average age of family = 18 years

Therefore, the total age of family(3 members) = 18 * 3 = 54 years

(At that time child age would be zero, so the age of father and mother would have increased by same.)

Its increased by 2 years for each = 50 + 2 + 2 = 54 years

When second child born the average age of family = 15 years

Therefore, the total age of family(4 members) = 15 * 4 = 60 years

(So, at that time second child age would be zero, the age of father, mother and first child would have increased by same.)

So its increased by 2 years for each = 54 + 2 + 2 + 2 = 60 years.

Therefore after 4 years, the total age of couple (from age of 50) = 50 + 4 + 4 = 58 years

So, the average age of couple = 58/2 = 29 years.

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