Answer: Option C. -> 6 years
Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.
∴ Required difference = (42 - 36) years = 6 years.

Answer: Option B. -> 7 : 3
Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
⇒ 3x + 20 = 2x + 40
⇒ x = 20
∴ Required ratio
= (3x + 10) : (x + 10)
= 70 : 30
= 7 : 3

Answer: Option A. -> 16 years
Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years Then,
$$\eqalign{
& \frac{{\left( {6x + 6} \right) + 4}}{{\left( {5x + 6} \right) + 4}} = \frac{{11}}{{10}} \cr
& \Rightarrow \frac{{6x + 10}}{{5x + 10}} = \frac{{11}}{{10}} \cr
& \Rightarrow 10\left( {6x + 10} \right) = 11\left( {5x + 10} \right) \cr
& \Rightarrow 60x + 100 = 55x + 100 \cr
& \Rightarrow 5x = 10 \cr
& \Rightarrow x = 2 \cr} $$
Sagar's present age = (5x + 6) years = (5 × 2 + 6) years = 16 years

Answer: Option A. -> $${\text{6}}\frac{2}{3}{\text{ }}$$ years
Vimal's present age = (8 + 2) years = 10 years
Sneh's father's age = 2(10 + 10) years = 40 years
Sneh's age
$$\eqalign{
& {\text{ = }}\left( {\frac{1}{6} \times 40} \right){\text{ years }} \cr
& {\text{ = }}\frac{{20}}{3}{\text{years }} \cr
& {\text{ = 6}}\frac{2}{3}{\text{years}} \cr} $$

Answer: Option B. -> 23 years
Let the age of the son and the daughter of Poorvi be 6a years and 7a years respectively.
5 years hence, present age of son = 6a - 5 and present age of daughter = 7a - 5
According to the question,
Eight years ago, the age of Poorvi = 6a - 5 + 7a - 5 = 13a - 10
So, present age of Poorvi = 13a - 10 + 8 = 13a - 2
Since, present age of Poorvi husband = 3 (6a - 5)
The difference of present age of Poorvi husband and Poorvi = 7 (Given)
$$\eqalign{
& {\text{3}}\left( {6a - 5} \right) - \left( {13a - 2} \right) = 7 \cr
& \Rightarrow 18a - 15 - 13a + 2 = 7 \cr
& \Rightarrow 5a = 20 \cr
& \Rightarrow a = 4 \cr} $$
The present age of daughter
= (7a - 5)
= 7 × 4 - 5
= 23 years

Answer: Option D. -> 18 years
Let the present age of Y be a years
Three years ago X's age = 3a years
Then, present age of X is (3a + 3)
Z's present age = 2a
According to question
Now, (3a + 3) - 2a = 12
a = 9 year
∴ Present age of Z = 2a = 2 × 9 = 18 years

Answer: Option B. -> 5 years
Let Sulekha age be 9 year,Then Arunima's age = 8x years
$$\eqalign{
& \frac{{9x + 5}}{{8x + 5}} = \frac{{10}}{9} \cr
& \Rightarrow 9\left( {9x + 5} \right) = 10\left( {8x + 5} \right) \cr
& \Rightarrow 81x + 45 = 80x + 50 \cr
& \Rightarrow x = 5 \cr} $$
Difference in their ages = (9x - 8x) years = x years = 5 years

Answer: Option B. -> 8 : 7
$$\eqalign{
& {\text{A's age = }}\left( {44 \times \frac{6}{{11}}} \right){\text{years}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 24 years}} \cr
& {\text{And B's age = }}\left( {44 - 24} \right){\text{years}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 20 years}} \cr} $$
Ratio of their ages after 8 years
$$\eqalign{
& {\text{ = }}\frac{{\left( {24 + 8} \right)}}{{\left( {20 + 8} \right)}} \cr
& = \frac{{32}}{{28}} \cr
& = \frac{8}{7} \cr
& = 8:7 \cr} $$

Answer: Option A. -> 3 Years
Let Nishi's age be 6x years,
Then Vinnee's age = 5x years
$$\eqalign{
& \therefore \frac{{6x + 9}}{{5x + 9}} = \frac{9}{8} \cr
& \Rightarrow 8\left( {6x + 9} \right) = 9\left( {5x + 9} \right) \cr
& \Rightarrow 48x - 45x = 81 - 72 \cr
& \Rightarrow 3x = 9 \cr
& \Rightarrow x = 3 \cr
& {\text{Difference in their ages}} \cr
& {\text{ = }}\left( {6x - 5x} \right) \cr
& = x {\text{ years}} \cr
& = {\text{3 years}} \cr} $$

Answer: Option A. -> 2 Years
Let Shakti's age be 8$$x$$ years,
Then Kanti's age = 7$$x$$ years
$$\eqalign{
& \therefore \frac{{8x + 10}}{{7x + 10}} = \frac{{13}}{{12}} \cr
& \Rightarrow 12\left( {8x + 10} \right) = 13\left( {7x + 10} \right) \cr
& \Rightarrow 96x + 120 = 91x + 130 \cr
& \Rightarrow 5x = 10 \cr
& \Rightarrow x = 2 \cr} $$
Difference between their ages
$$\eqalign{
& = \left( {8x - 7x} \right) \cr
& = {\text{ }}x\,{\text{years}} \cr
& {\text{ = 2}}\,{\text{years}} \cr} $$