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Solution :

Given :

Two years ago the son celebrated his tenth birthday ∴ Present age of the son = (10 + 2) years = 12 years

Calculations :

Let the present age of Father , Son and Daughter be F , S and D respectively.

Also the ratio of age of son to father six year from now is 3 : 7

Six year from now the ages of father and son be (F+6) and (S+6) respectively.

⇒ (S+6)/(F+6) = 3/7 ----(1)

⇒ Putting S = 12, in equation (1),

⇒ (12 + 6)/(F+6) = 3/7

⇒ 3 F + 18 = 126

⇒ F = 36 years

It is given that, the sum of present ages of son and daughter is 14 years less than the father’s age.

⇒ S + D = F – 14 ----(2)

Putting S = 12 and F = 36 in equation (2),

⇒ 12 + D = 36 – 14

⇒ D = 36 – 14 – 12

⇒ D = 10 years

Hence the present age of daughter is 10 years.

Given:

Father’s present age + Son’s present age = 52 years

Son’s age after 4 years = 1/4 × Father’s age after 4 years

Concept used:

Using the concept of the linear equation.

Calculation:

Let the present age of the son be x years.

And the present age of the father is (52 – x) years.

According to the question,

Son’s age after 4 years = 1/4 × Father’s age after 4 years

⇒ (x + 4) = 1/4 × (52 – x + 4)

⇒ (x + 4) × 4 = 56 – x

⇒ 4x + 16 = 56 – x

⇒ 5x = 40

⇒ x = 8 years

Son’s present age = 8 years

Father’s present age = 52 – 8

⇒ Father’s present age = 44 years

Required ratio = (Age of son after 10 years)/(Age of father after 10 years)

⇒ Required ratio = (8 + 10)/(44 + 10)

⇒ Required ratio = 18/54

⇒ Required ratio = 1/3

∴ The ratio of the age of the son and father, 10 years from now is 1 ∶ 3.

Given:

Present age of Kalyani is 9 times her son’s age.

11 years hence, the ratio of the ages of Kalyani and her son = 12 : 5

Calculation:

Let the present age of son be x

⇒ Present age of Kalyani be 9x

⇒ (x + 11)/(9x + 11) = 5/12

⇒ 12(x + 11) = 5(9x + 11)

⇒ 12x + 132 = 45x + 55

⇒ 45x – 12x = 132 – 55

⇒ 33x = 77

⇒ x = 77/33

⇒ x = 7/3

Present age of Kalyani =9 × (7/3) years

⇒ 21 years

∴ Present age of Kalyani is 21 years

The ratio age of father 2 years and son 4 years after is 10∶ 3

⇒ The present age of the father = 10x– 2

The present age of the son = 3x– 4

The present age of the mother is 4 times that of son

⇒ Present age of the mother = 4(3x– 4) = 12x– 16

The age of the father 3 years ago is same as the age of the mother 3 years after

⇒ 10x– 2 – 3 = 12x– 16 + 3

⇒ 2x = 8

⇒ x = 4

∴ The present age of the mother = 12× 4– 16 = 32

The present age of the son = 3× 4– 4 = 8

∴ The ratio of age of motherafter 3 years and sonafter 2 years

⇒ (32 + 3)/(8 + 2) = 35/10 = 7/2or 7∶ 2

∴ The ratio of age of motherafter 3 years and sonafter 2 years is 7∶ 2

Given that :

Son's age 5 years ago = 16 years.

Son's present age = 16 + 5 = 21 years.

According to statement given,.

Mother's age when son was born (21 years ago) = Present age of son.

Mother's age 21 years ago = 21 years.

Mother's present age = 21 + 21 = 42 years.

Hence, the correct answer is "42 years".

Given:

Average age = 40 years

Formula used:

Average = Sum of all the terms/Total number of terms

Calculation:

A∶ B =3∶ 4

And, B∶C =4∶5

Then, A∶ B∶ C = 3∶ 4∶ 5

Let the age of A, B and C be 3x, 4x and 5x

Sum of ages of all the persons = 3x + 4x + 5x = 12x

Average = 12x/3 = 4x

⇒ 4x = 40

⇒ x = 10

∴ The age of B is 40

Given:

The average age of a family of 9 members is 20 years.

The age of the youngest son of the family is 8 years.

Calculation:

According to the question,

Sum of present ages of 9members

⇒ 20× 9

⇒ 180 years

Total age of a members 8 years ago

⇒ 180– (9× 8)

⇒ 108 years

The average age of the members of the family just before the birth

⇒ 108/8

⇒ 13.5 years

∴ The average age of the members of the family just before the birth of the youngest son was 13.5 years.

Given:

The average of ages of P and Q is 24years.

Average age of P, Q and R is 22 years.

Formula:

If average age of A and B after x years is y, present average age = y - x

Calculation:

Let the present ages be P, Q and R respectively.

(P + Q)/2 = 24

⇒ (P + Q)= 48 ----(i)

(P + Q + R)/3 = 22

⇒ (P + Q + R) = 66 ----(ii)

From above equation we only get the sum of ages but information is not available about time, like present age, after some years and before some years.