Let Samina's present age be 7x and Suhana's present age be 3x.

After 6 years, Samina's age will be 7x+6 and Suhana's age will be 3x+6.

Then, (7x + 6) : (3x + 6) = 5 : 3

       Þ3(7x + 6) = 5 (3x + 6)

       Þ21x + 18 = 15x + 30

       Þ6x = 12

       Þx= 2​

Now, difference in their ages = 7x – 3x = 4x = 4 × 2 = 8.

Let P be Poorvi's present age, S be the present age of her son, D be the present age of her daughter & H be Poorvi's husband's present age.

Eight years ago, Poorvi's age was P−8.

The sum of the present ages of her son and daughter is S+D.

Then, P−8 = S+D ………… (i)

Five years hence, the daughter's age will be D+5 and the son's age will be S+5.

Then, 6(D+5) ​= 7(S+5)

Þ 6D+30 = 7S+35

Þ 6D−7S = 5 ………… (ii)  

Poorvi's husband is 7 years elder to her, so H=P+7.

His present age is three times the present age of their son, so H = 3S.

                                                                                             Þ P+7=3S

                                                                                             Þ P = 3S−7 ………….(iii)  

Substituting value of P into equation (iii),

Þ 3S−7−8 = S+D

Þ 3S−15 = S+D

Þ 2S−D = 15

Þ D = 2S – 15 ………… (iv)

Substituting value of D into equation (ii),

       6(2S−15)−7S=5

 Þ 12S−90−7S=5

 Þ 5S=95

 Þ S=19

Now, substitute S=19 into equation (iv)

      D = 2S−15

Þ D = 2(19) −15

Þ D = 38 −15

Þ D = 23  

Let F be the present age of the father, S be the present age of the son, and M be the present age of the mother.

Then, F+S = M+8

     Þ M = S+22

We need to find F+4.

Substitute equation (2) into equation (1):

     F+S = (S+22) + 8

Þ F + S = S+30

Þ F=30

Father's age after 4 years = F+4 = 30 + 4 = 34

Let, Rahul, Sagar & Purav’s age = x, y & z.

Then, y−x = x−z

     Þ 2x = y + z  

Sum of Sagar and Purav’s ages

          y+z = 66

Now, 2x = y + z

     Þ 2x = 66 (Since y + z = 66)

     Þ x = 33

So, Rahul's age is 33 years.

We need to find x-z:

          x- z = 33 - z

From given options, if z=18, we substitute:

         x-z = 33−18 =15

\ The difference between Rahul's and Purav’s age is 15 years.

Let Simmi’s and Niti’s present ages be S and N.

Then, ten years hence

     9(S + 10) = 7(N + 10)​
Þ 9S−7N=−20

Again, two years ago

     3(S – 2) = N – 2

Þ 3S−N=4

Þ N = 3S – 4

Substituting value of N,

     9S−7N= −20

Þ 9S−7(3S−4)= −20

Þ -12S + 28 = - 20

Þ S = 4

 \ N=3(4) – 4 = 8

Hence, Abhay’s present age

 A = N + 4 = 8 + 4 = 12

Let A's and B's ages 4 years ago be A−4 and B−4.

Then, ½ × 12(A−4) = 5 × 4(B−4) ​

      Þ 6A−24 =−20B – 80

      Þ  6A + 20B = - 80 + 24

      Þ 3A + 10B = - 28

& A + 8 = 2(B + 6)

Þ A – 2B = 4

Þ A = 4 – 2B

Substituting the value of A, 3A−10B=−28

                                             ⇒ 3(2B+4)−10B=−28

                                             ⇒ 6B + 12 − 10B = −28

                                                   ⇒ −4B = − 40

                                                   ⇒ B =10

\ B's present age is 10 years.