Answer: Option D. -> 22 years
Let the son's present age be x years. Then, man's present age = (x + 24) years.
∴ (x + 24) + 2 = 2(x + 2)
⇒ x + 26 = 2x + 4
⇒ x = 22

Answer: Option D. -> 20 years
Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
⇒ 54 - x = 5x - 30
⇒ 6x = 84
⇒ x = 14
∴ Son's age after 6 years = (x + 6) = 20 years.

Answer: Option D. -> 24.5 years
$$\eqalign{
& {\text{Let}}\,{\text{Rahul's}}\,{\text{age}}\,{\text{be}}\,x\,{\text{years}}. \cr
& {\text{Then,}}\,{\text{Sachin's}}\,{\text{age}} = \left( {x - 7} \right)\,{\text{years}}. \cr
& \therefore \frac{{x - 7}}{x} = \frac{7}{9} \cr
& \Rightarrow 9x - 63 = 7x \cr
& \Rightarrow 2x = 63 \cr
& \Rightarrow x = 31.5 \cr
& {\text{Hence,}}\,{\text{Sachin's}}\,{\text{age}} \cr
& = \left( {x - 7} \right)\,{\text{years}} \cr
& = 24.5\,{\text{years}} \cr} $$

Answer: Option B. -> 15 years
Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,
4x + 6 = 26
⇒ 4x = 20
⇒ x = 5
∴ Deepak's age = 3x = 15 years.

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

Answer: Option B. -> 3 : 1
Let A's age be 5x years, then B's age = 3x years
$$\eqalign{
& \frac{{5x - 4}}{{3x + 4}} = \frac{1}{1} \cr
& \Rightarrow 5x - 4 = 3x + 4 \cr
& \Rightarrow 2x = 8 \cr
& \Rightarrow x = 4 \cr
& \therefore \frac{{{\text{A's age 4 years hence}}}}{{{\text{B's age 4 years ago }}}} \cr
& = \frac{{5x + 4}}{{3x - 4}} \cr
& = \frac{{5 \times 4 + 4}}{{3 \times 4 - 4}} \cr
& = \frac{{24}}{8} \cr
& = \frac{3}{1} \cr
& = 3:1 \cr} $$

Answer: Option D. -> 108 years
Let the son's age 18 years ago be x years, Then man's age 18 years ago = 3x years
$$\eqalign{
& \left( {3x + 18} \right) = 2\left( {x + 18} \right) \cr
& \Rightarrow 3x + 18 = 2x + 36 \cr
& \Rightarrow x = 18 \cr} $$
Sum of their present ages
$$\eqalign{
& \Rightarrow \left( {3x + 18 + x + 18} \right){\text{years}} \cr
& \Rightarrow \left( {4x + 36} \right){\text{years}} \cr
& \Rightarrow \left( {4 \times 18 + 36} \right){\text{years}} \cr
& \Rightarrow {\text{ 108 years}} \cr} $$

Answer: Option B. -> 7 : 3
Let son's age 10 years ago be x years, Then man's age 10 years ago = 3x years
Son's present age = (x + 10) years , Man's present age = (3x + 10) years
$$\eqalign{
& \left( {3x + 10} \right) + 10 = 2\left( {x + 10 + 10} \right) \cr
& \Rightarrow 3x + 20 = 2\left( {x + 20} \right) \cr
& \Rightarrow 3x + 20 = 2x + 40 \cr
& \Rightarrow x = 20 \cr} $$
Ratio of present ages of man and the son
$$\eqalign{
& {\text{ = }}\frac{{3x + 10}}{{x + 10}} \cr
& = \frac{{3 \times 20 + 10}}{{20 + 10}} \cr
& = \frac{{70}}{{30}} \cr
& = 7:3 \cr} $$

Answer: Option D. -> None of these
16 years ago, let T = x years and G = 8x years
After 8 years from now, T = (x + 16 + 8) years and G = (8x + 16 + 8) years
$$\eqalign{
& \therefore {\text{8x + 24 = 3}}\left( {x + 24} \right) \cr
& \Rightarrow 8x - 3x = 72 - 24 \cr
& \Rightarrow 5x = 48 \cr
& 8{\text{years ago,}} \cr
& {\text{ }}\frac{{\text{T}}}{{\text{G}}} \cr
& = \frac{{x + 8}}{{8x + 8}} \cr
& = \frac{{\frac{{48}}{5} + 8}}{{8 \times \frac{{48}}{5} + 8}} \cr
& = \frac{{48 + 40}}{{384 + 40}} \cr
& = \frac{{88}}{{424}} \cr
& = \frac{{11}}{{53}} \cr} $$

Answer: Option D. -> Cannot be determined
Let Neelam's age be 5x years and Shiny's age be 6x years
$$\eqalign{
& \left( {\frac{1}{3} \times 5x} \right):\left( {\frac{1}{2} \times 6x} \right) = 5:9 \cr
& \Rightarrow \frac{{5x}}{{3 \times 3x}} = \frac{5}{9} \cr} $$
Thus, Shiny's age cannot be determined