Answer: Option A. -> 12 Years
Let the daughter's age be x years. Then, mother age = 3x years
3x + 12 = 2 (x + 12)
⇒ 3x + 12 = 2x + 24
⇒ x = 12
Present age of daughter = 12 years

Answer: Option B. -> 3 Years
Let Farah's age 8 years ago be x years. Then , her present age = (x + 8)
$$\eqalign{
& \therefore x + 8 = \frac{9}{7}x \cr
& \Rightarrow 7x + 56 = 9x \cr
& \Rightarrow 2x = 56 \cr
& \Rightarrow x = 28 \cr} $$
∴ Farah's age now
= (x + 8) years
= (28 + 8) years
= 36
Her daughter's age now
=$$\left( {\frac{1}{6} \times 36} \right)$$   years
= 6 years
Her daughter's age 3 years ago
= (6 - 3) years
= 3 years

Answer: Option C. -> 54 years
Let the son's age be $$x$$ years , Then Mr. Sanyal's age = 3$$x$$ years
$$\eqalign{
& \therefore \frac{{3x + 6}}{{x + 6}} = \frac{5}{2} \cr
& \Rightarrow 2\left( {3x + 6} \right) = 5\left( {x + 6} \right) \cr
& \Rightarrow 6x + 12 = 5x + 30 \cr
& \Rightarrow x = 18 \cr} $$
∴ Present age of Mr. Sanyal = 3x years
= (3 × 18) years
= 54 years

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

Answer: Option E. -> None of these
Average age of man and his daughter = 34 years
Their total age = (34 × 2) years = 68 years
Let man's age be x years, Then daughter age = (68 - x) years
$$\eqalign{
& \therefore \frac{{x + 4}}{{68 - x + 4}} = \frac{{14}}{5} \cr
& \Rightarrow 5\left( {x + 4} \right) = 14\left( {72 - x} \right) \cr
& \Rightarrow 5x + 20 = 1008 - 14x \cr
& \Rightarrow 19x = 988 \cr
& \Rightarrow x = 52 \cr} $$
∴ Daughter's present age = (68 - 52) years = 16 years
Alternate Solution :
According to question,
After 4 years, the total age of man & daughter is
= [(34 × 2) + 4 + 4]
= 76 years
After 4 years their age ratio is 14 : 5 (given)
So, 4 years after the daughter age will be
= 76 × $$\frac{5}{19}$$
= 20 years
∴ Daughter present age
= 20 - 4
= 16 years

Answer: Option B. -> 40 years
Let daughter's age be x years. Suresh's age = 2x years
$$\eqalign{
& \therefore \frac{{2x + 6}}{{x + 6}} = \frac{{23}}{{13}} \cr
& \Rightarrow 13\left( {2x + 6} \right) = 23\left( {x + 6} \right) \cr
& \Rightarrow 26x + 78 = 23x + 138 \cr
& \Rightarrow 3x = 60 \cr
& \Rightarrow x = 20 \cr} $$
Present age of Suresh = 2x years
$$\eqalign{
& {\text{ = }}\left( {2 \times 20} \right){\text{ years }} \cr
& {\text{ = 40 years}} \cr} $$

Answer: Option C. -> 14 years
Let son's age 10 years ago be x years.
Then, man's age 10 years ago = 7x years
Son's present age = (x + 10) years, Man's present age = (7x + 10) years
$$\eqalign{
& \therefore {\text{2}}\left[ {\left( {7x + 10} \right) + 2} \right]{\text{ = 5}}\left[ {\left( {x + 10} \right) + 2} \right] \cr
& \Rightarrow 2\left( {7x + 12} \right) = 5\left( {x + 12} \right) \cr
& \Rightarrow 14x + 24 = 5x + 60 \cr
& \Rightarrow 9x = 36 \cr
& \Rightarrow x = 4 \cr} $$
Son's present age = (x + 10) years = (4 + 10) years = 14 years

Answer: Option B. -> 8 years
Let Samina's age be 7x years. Then, Suhana's age = 3x years
$$\eqalign{
& \therefore \frac{{7x + 6}}{{3x + 6}} = \frac{5}{3} \cr
& \Rightarrow 3\left( {7x + 6} \right) = 5\left( {3x + 6} \right) \cr
& \Rightarrow 21x + 18 = 15x + 30 \cr
& \Rightarrow 6x + 12 \cr
& \Rightarrow x = 2 \cr} $$
Difference in their ages = (7x - 3x) years = 4x years = (4 × 2) years = 8 years

Answer: Option C. -> 31 years
Let A's age be 5x years.
Then, B's age = 6x years
$$\eqalign{
& \therefore \frac{{5x + 6}}{{6x + 6}} = \frac{6}{7} \cr
& \Rightarrow 7\left( {5x + 6} \right) = 6\left( {6x + 6} \right) \cr
& \Rightarrow 35x + 42 = 36x + 36 \cr
& \Rightarrow x = 6 \cr} $$
B's age 5 years ago = (6x - 5) years = (6 × 6 - 5) years = 31 years

Answer: Option B. -> 8 years
$$\eqalign{
& {\text{Ram's father's age}} \cr
& {\text{ = 50 years, }} \cr
& {\text{Ram's age}} \cr
& {\text{ = }}\left( {\frac{3}{5} \times 50} \right){\text{years}} \cr
& {\text{ = 30 years}} \cr
& {\text{Ram's wife's age}} \cr
& {\text{ = }}\left( {\frac{4}{5} \times 30} \right){\text{years}} \cr
& {\text{ = 24 years}} \cr
& {\text{Ram's son's age}} \cr
& {\text{ = }}\left( {\frac{1}{3} \times 24} \right){\text{years}} \cr
& {\text{ = 8 years}} \cr} $$