Five years hence,

Let the present age of Anjali be x and of Dimple be y.

Five years hence,

Age of Anjali = (x + 5) years

Age of Dimple = (y + 5) years

Age of Anjali = 3(Age of Dimple)

x + 5 = 3(y + 5)

x + 5 = 3y + 15

x – 3y = 10……(1)

Five years ago,

Age of Anjali = (x – 5)

Age of Dimple = (y – 5)

Age of Anjali = 7(Age of Dimple)

x – 5 = 7(y – 5)

x – 5 = 7y – 35

x – 7y = -30……(2)

Subtracting equation 2 from equation 1, we get,

(x – 3y) – (x – 7y) = 10 – (-30)

x – 3y – x + 7y = 10 + 30

4y = 40

y = 10 years

Putting the value of ‘y’ in equation 1, we get,

x – 3 × 10 = 10

x – 30 = 10

x = 40 years

Hence, the age of Anjali is 40 years and age of Dimple is 10 years.

OR

Let

2x – y = 11 …..(1)

x + y = 25….(2)

Multiplying equation 2 with 2, we get,

2(x + y) = 2 × 25

2x + 2y = 50…..(3)

Subtracting equation 2 from equation 3, we get,

(2x + 2y) – (2x - y) = 50 – 11

2x + 2y – 2x + y = 39

3y = 39

y = 13

Putting the value of ‘y’ in equation (2), we get,

x + 13 = 25

x = 12

Therefore, x = 12 and y = 13

Now, k = (13 – 12)³ = (1)³ = 1

Hence, the value of k is 1