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Given :

The average age of father and son =25 years.

Solution:

Let the present age of father and son be F and S respectively.

⇒ (F + S)/2 = 25

⇒ F + S = 50 ----(1)

Also, thrice the age of son is less than father’s age by two years.

⇒ 3S = F – 2

⇒ F – 3S = 2 ----(2)

From equation(2), we get:

F = 2 + 3S ----(3)

Using equation(3) in equation (1), we get:

⇒2 + 3S+ S = 50

⇒ 4S= 48

⇒ S = 48/4 = 12

∴ The age of the son is 12 years.

Calculation:

Let present age of mother is x, then present age of his son= 2x/5

After 8 year,

Son's age = (2x/5 + 8)years

Mother's age = (x + 8)years

According to the question:

Son's age is1/2 time of mother's

2x/5 + 8 = 1/2(x + 8)

⇒ (2x + 40)/5= x/2 + 4

⇒(2x + 40)/5= (x + 8)/2

⇒ 4x + 80 = 5x + 40

⇒ x = 40years

∴ Present ageof mother is 40 years.

Calculation:

Let, Tanya's present age be x years

and Tanya's grandfather's age be y years

Tanya's age 16 years ago = x − 16 years

Tanya's grandfather's age = y − 16 years

According to the question:

y − 16 = 8(x − 16)

⇒ y − 16 = 8x − 128

⇒ y = 8x − 128+ 16

⇒ y = 8x − 112 ----(1)

Tanya's age, 8 years from now = x + 8

Tanya's grandfather's age, 8 years from now = y + 8

Again,According to the question:

y + 8 = 3(x + 8)

⇒ 8x − 112 + 8 = 3(x + 8)

⇒ 8x − 104 = 3x + 24

⇒ 8x − 3x = 24 + 104

⇒ 5x = 128

⇒ x= 128/5

Putting the value of x = 128/5 in equation(1):

y = 8x − 112

⇒ y = 8× 128/5 - 112

⇒ y = (1024 - 560)/5 = 464/5

Tanya's age, 8 years ago

⇒128/5 - 8 = 88/5

Tanya's grandfather's age, 8 years ago

464/5 - 8 = 424/5

Ratio of Tanya's age to Tanya's grandfather's age = 88 : 424 = 11 : 53

∴ The ratio of Tanya's age to that of her grandfather is 11 : 53.

Given:

After five years the age of father will be three times of the age of the son.

Five yearsago father’s age was seven times of the age of his son.

Calculation:

Let the age of son after 5 years be x.

Then, the age of father after 5 years be 3x.

The present age of son = x - 5

The present age of father = 3x - 5

The age of son 5 years ago = x - 5 - 5 = x - 10

The age of father5 years ago = 3x - 5-5 = 3x - 10

According to the question;

⇒ 7(x - 10) = 3x - 10

⇒ 7x - 70 = 3x - 10

⇒ 4x = 60

⇒ x = 15

The present age of son = 15 - 5 = 10 years

The present age of father = 3× 15 - 5 = 40 years

∴ Thepresent ages of father and son is 40 years and 10 years.

Given:

4 years ago, Father's age =3× Son's age

Sum of Father's age and Son's age = 64 years

Calculation:

Let the Father's present age and Son's present age be x years and y years respectively

According to the question

Four years ago, father's age = 3× Son's age

⇒ (x − 4) = (y − 4) × 3

⇒ x = 3y − 8 ----(1)

After 4 years, Sum of Father's age and Son's age= 64

⇒ (x + 4) + (y + 4) = 64

⇒ x + y = 56

⇒ y = 56 - x ----(2)

Putting the value of y inequation (1), we get

x = 3y − 8

⇒ x = 3(56 - x) - 8

⇒ x =3 × 56 − 3x − 8

⇒ 4x = 160

⇒ x = 160/4 = 40

∴ The Father's present age is 40 years.

Calculation:

Let the present age of the son be x years then the present age of the father be 2x

20 years back,

The age of the father = 2x –20 years

The age of the son = x –20 years

Now, A/Q

2x –20 = 12(x –20)

⇒ 2x –20 = 12x –240

⇒ 12x –2x = 240 –20

⇒ 10x = 220

⇒ x = 22

∴ The age of the son and the father are 22 years and 44 years respectively

Given:

Let father's present age be a and son's present age be b.

⇒ (a - 15) = 2(b - 15)

⇒ (a + 5) = 1.5(b + 5)

Calculation:

⇒ a - 15 = 2b - 30

⇒ 2b - a = 15

Then,

⇒ a + 5 = 1.5b + 7.5

⇒ a - 1.5b = 2.5

Solving,

⇒ 2b - 2.5 - 1.5b = 15

⇒ b = 35 years

⇒ a = 55 years

∴ Ratio of present age of father and son = 55 : 35 = 11 : 7

Given:

The sum of their ages is 64 years old

After 10 years, the age of father will be twice the age of his son

Calculations:

Let the age of father be ‘x’ years old

Let the age of son be ‘y’ years old

After 10 years,

The age of father will be (x + 10) years old

The age of son will be (y + 10) years old

According to question, we have

⇒ x + 10 = 2(y + 10)

⇒ x + 10 = 2y + 20

⇒ x – 2y = 10 ----(1)

And, x + y = 64 ----(2)

From (1) and (2), we get

⇒ y = 18 years

So, the age of son is 18 years old

Put y = 18 in equation (2), we get

⇒ x = 46 years

So, the age of father is 46 years old

Difference between their ages is

⇒ 46 – 18 = 28 years

∴ The difference between the ages of father and son is 28 years.

Given :

The sum of ages of a father and son = 45 years

Five years ago, the product of their ages was four times the father's age at that time.

calculation :

Let the age of father be (a)years and age of his son be (45 - a) years,

Five years ago,

Age of father = (a - 5) years

Age of his son = (45 - a - 5) years = (40 -a) years

According to the question,

Product of their ages five years ago = 4× father's age five years ago

⇒ (a - 5) (40 - a) = 4(a - 5)

⇒ (a - 5) (40 - a) = 4(a - 5)

⇒ 40 - a = 4

⇒ 40 - 4 = a

⇒ 36 = a

Hence,

Present age of father = a years = 36 years

Present age of his son = (45 - a) = (45 -36) = 9 years

Difference between of father's age and son's age = 36 - 9 = 27

∴The twice the difference, of father and son's age is2× 27 = 54

GIVEN:

Age at marriage = Present age - 5

Present age = 6/5× Age at marriage

CALCULATIONS:

Let her age at the time of marriage be x years.

⇒Present age = (x + 5) years

A.T.Q

x + 5 = 6x/5

⇒ 5x + 25 = 6x

⇒ x = 25 years

Now, Son was born after three years of marriage

⇒ Required age = 25 + 3 = 28 years

∴ The age of Swati when her son was born was 28 years.

Given∶

A’s age is reduced by 5 years and B’s age is increased by 3 years, then the product of their ages is reduced by 9.

Also, if we increase A’s age by 3 years and B’s age by 2 years, then the product of their ages is increased by 67.

Formula Used∶

Concept of Linear Equations, Elimination Method.

Calculation∶

Let the ages of A and B be ‘x’ and ‘y’ years.

Then the product of their ages = xy

According to question,

(x - 5)(y + 3) = xy – 9

⇒ 3x – 5y – 6 = 0 ----(1)

Also, (x + 3)(y + 2) = xy + 67

⇒ 2x + 3y - 61 = 0 ----(2)

On multiplying eq.(1) by 2 and eq.(2) by 3, we get

6x – 10y – 12 = 0 ----(3)

6x + 9y – 183 = 0 ----(4)

Subtracting eq. (3) from (4), we get

19y – 171 = 0

⇒ y = 9

Substitute the value of y = 9 in eq.(2), we get

2x + 3(9) – 61 = 0

⇒ 2x + 27 – 61 = 0

⇒ 2x = 34

⇒ x = 17

Hence, A’s age is 17 years and B’s age is 9 years.

Given

Dinesh was married at the age = 27 years

Formula Used

Average = sum of data/No. of data

Calculation

Total age of Dinesh, his wife and his son after 6 years of marriage= 22×3 = 66 years

⇒ According to Question

⇒ 33 + 29 + x = 66

⇒ x = 4

So, his son after 6 years of marriage = 4 years

then, his son was born 2 years after marriage

∴ The Dinesh's son born after 2 years ofhis marriage

GIVEN:

(Man + wife)'s average age at marriage = 27 yrs

Child's age after 4 years of marriage = 1 yr

FORMULA USED:
Average = Sum of observations/Total number of observations

CALCULATION:
(Man + wife)'s age at marriage = 27× 2 = 54 yrs

(Man + wife)'s age after 4 yrs= 54 + 4 × 2 = 62 yrs

Total age of family = 62 + 1 = 63 yrs

Average age = 63/3 = 21 yrs

∴ The average age is 21 years.

GIVEN:

Average of 6 members = 44 yrs

Age of youngest member = 14 yrs

FORMULA USED:

Average = Sum of observations/Total number of observations

CALCULATION:

Total age of the family = 44×6 = 264 yrs

Total age at the birth of youngest member = 264 - (14 × 6) = 180 yrs

At that time there were only 5 members,

∴ Required average = 180/5 = 36 yrs

∴ Average age of the family was 36 years.

At the birth of the youngest memberis a standard line in such age-related questions so you have to exclude the child as unborn.

Given:

Average age of 5 members = 55 yrs

Average age of 7 members = 47 yrs

Formula used:

Average = Sum of observations/Total number of observations

Calculations:

Total age of 5 members = 55×5 = 275 yrs

After 5 years total age of 5 members = 275 + 25 = 300

Baby's age = 2 yrs (as it was born after 3 years of marriage)

Current total age,

300 + 2 + wife's age = 47× 7 = 329

wife's age = 27 yrs

Age at time of marriage = 27 - 5 = 22 yrs

∴ The answer is 22 years.

GIVEN:

Ages are consecutive odd numbers.

Youngest : Oldest (5 years ago) = 4 : 5

EXPLANATION:
Let the ages be x, x + 2, x + 4

A.T.Q

(x - 5)/(x + 4 - 5) = 4/5

⇒ 5x - 25 = 4x - 4

⇒ x = 21 years

Required age = 21 + 2 + 2 = 25 years

∴ The answer is 25 years.

Calculations:

Total age of 3 girls = 3 × 22

⇒ 66

Ratio of their ages = 5 : 8 : 9

∴ Age of the youngest girl = 5/22 × 66

⇒ 5 × 3

⇒ 15 years

∴ Age of the oldest girl = 9/22 × 66

⇒ 9 × 3

⇒ 27 years

Given:

Ratio of ages of Nitin and Mayuri =5 : 6

Ratio between one-third age of Nitin and half of Mayuri’s age = 5 : 9

Calculations:

Let the school ages of Nitin and Mayuri be 5x and 6x respectively.

Hence, the ratio between them according to the second given condition is:

⇒ (5x/3)/(6x/2)= 5/9

⇒ 10x/18x = 5/9

⇒ 15 = 15

∴ Mayuri’s age cannot be determined.

We need to have the relation betweenthe ages of the persons after or before a certain number of years. If that relation is not provided, the relation cannot be established.

Calculations:

Let the present age of Neha be 7x.

Let the present age of Nikita be 6x.

∴ According to the question:

⇒ 7x + 6x = 52

⇒ 13x = 52

⇒ x = 4

∴ Neha’s present age = 7 × 4

⇒ 28 years

∴ Neha’s present age = 6 × 4

⇒ 24 years

∴ required ratio after 12 years :

⇒ 28 + 12 : 24 + 12

⇒ 40 : 36

⇒ 10 : 9

The respective ratio of their ages 12 years later is 10 : 9.