Let the present age of A be 5x and the present age of B be 3x.

Then, A's age 4 years ago was 5x−4.

          B's age 4 years hence will be 3x+4.

According to question,

       (3x+4) : (5x−4) = 1 : 1

​  ⟹ 5x−4 = 3x+4

  ⟹ 5x−3x = 4+4

  ⟹ 2x = 8

  ⟹ x = 4

Thus, A's present age is 5x = 5(4) = 20 years, and B's present age is 3x = 3(4) = 12 years.

Again, A's age 4 years hence will be 20+4=24 years.

           B's age 4 years ago was 12−4=8 years.

\ The ratio between A's age 4 years hence and B's age 4 years ago is 8 : 24 = 1:3

​

Let the present age of the man be 4x and his wife be 3x.

After 4 years, the man's age will be 4x+4 and the wife's age will be 3x+4.

Then, (4x+4) : (3x+4) = 9 : 7

​  ⟹ 7(4x+4) = 9(3x+4)

  ⟹ 28x+28 = 27x+36

  ⟹ 28x−27x = 36−28

  ⟹ x = 8

Therefore, the present age of the man is 4x = 4(8) = 32 years, and the present age of the wife is 3x = 3(8) = 24 years.

Let y years ago they were married.

Then the man's age at the time of marriage was 32−y and the wife's age was 24−y.

So, (32−y) : (24−y) = 5 : 3

  ⟹ 3(32−y) = 5(24−y)

  ⟹ 96−3y = 120−5y

  ⟹ 5y−3y = 120−96

  ⟹ 2y = 24

  ⟹ y = 12

Hence, they were married 12 years ago.

Let, M = man's age & R = Ronit's age.

Then, M = 4R …….. (i)

          M + 8 = 2.5(R + 8)……….. (ii)

Substituting (i) into (ii),

        4R + 8 = 2.5R + 20

  ⟹ 1.5R = 12

  ⟹ R = 8

   \ M = 4 × 8 = 32

After 16 years,

Man = 32 + 16 = 48

Ronit = 8 + 16 = 24

Hence Ronit’s age would be 48 / 24 = 2 times.

Let P = Promila's current age & S = Sakahi's current age.

Then, one year ago P – 1 = 4(S – 1)

                          ⟹ P = 4S – 3

 and six years later P + 6 = S + 6 + 9

                          ⟹ P = S + 9

Equating P,   4S – 3 = S + 9

                ⟹ 3S = 12

                ⟹ S = 4

Substituting value of S,

           P = 4 + 9 = 13

\ Ratio of their present ages P : S = 13 : 4.

Let Tanya's current age be T and her grandfather's age be G.

16 years ago,

G −16 = 8(T−16)

⟹ G = 8T – 112 ……… (i)

8 years from now,

      G + 8 = 3(T + 8)
⟹ G = 3T + 16

Substituting value of G in equation (i)

8T−112 = 3T+16

5T = 128

T = 25.6

Similarly, G = 92.8

8 years ago, age of

Tanya = 25.6 – 8 = 17.6

Grandfather = 92.8 – 8 = 84.8

\ Ratio of their ages = 47.6 : 84.8 = 11:53

Let the present age of the elder man & younger man be E & Y respectively.
Then, E – Y = 10

Þ y = E – 10

15 years ago their ages

Elder man = E−15

Younger man = Y−15

According to question,

       E−15 = 2(Y−15)

Þ E−15 = 2(E−10−15) [Since Y = E−10]

Þ E - 15 = 2E – 50

Þ E = 35

Let Amisha's age 3 years ago be 8x and Nimisha's age 3 years ago be 9x.

Since this was 3 years ago, their present ages are

Amisha = 8x+3

Nimisha = 9x+3

Three years hence their ages

Amisha = (8x+3) + 3 = 8x+6

Nimisha = (9x+3) + 3 = 9x+6

According to question,

    (8x+6) : (9x+6) =11:12​

Þ12(8x+6) = 11(9x+6)

Þ96x + 72 = 99x + 66

Þ96x – 99x = 66 – 72

Þ3x = 6

Þx = 2

\ Amisha’s present age = 8x+3 = 8(2)+3 = 16+3 = 19.

Let Mr. Roy’s present age be R and Sachin’s present age be S.

Then, R – 10 = 14S ………. (i)

Again, Sachin is 9 years younger than Saloni, and Saloni’s age is 14 years.

So, S = 14 – 9 = 5

Substituting S = 5 into the equation (i),

    R−10=14 × 5

ÞR = 80.

Let Kunal's age 6 years ago be 6x and Sagar's age 6 years ago be 5x.

Since this was 6 years ago, their present ages are:

Kunal = 6x+6

Sagar = 5x+6

After four years their ages are

Kunal = (6x+6)+4=6x+10

Sagar = (5x+6)+4=5x+10

According to question,

     (6x+10) : (5x+10) = 11:10

Þ 10(6x+10) = 11(5x + 10)

Þ 60x – 55x = 110 – 100

Þ 5x = 10

Þ x = 2​

\ Sagar's present age = 5x+6=5(2)+6=10+6=16.

Let Sneh, her father & Vimal’s present age be S, F & V.

Then, S = 1/6 F ………….. (i)

     & F+10 = 2(V+10) ………… (ii)

Vimal's age 2 years ago was 8.

So, Vimal's present age is V = 8+2 = 10 years.

Substitute V=10 into equation (ii),

     F +10 = 2(10+10)

Þ F+10 = 2(20)

Þ F+10 = 40

Þ F = 30

Now, substitute F=30 into equation (i),

      S = 61​(30)

 Þ S = 5

Therefore, Sneh's present age is 5 years.