If 8 years ago from now, a grandmother’s age was 13 times the age of her granddaughter and after 12 years

Let the present age of grandmother = G
Let the present age of granddaughter = g

Condition 1

8 years ago:

Grandmother’s age = G - 8
Granddaughter’s age = g - 8

Given:

(G - 8) = 13(g - 8)

G - 8 = 13g - 104

G = 13g - 96 ...(1)

Condition 2

After 12 years:

Grandmother’s age = G + 12
Granddaughter’s age = g + 12

Given:

(G + 12) = 3(g + 12)

G + 12 = 3g + 36

G = 3g + 24 ...(2)

Solve (1) and (2)

13g - 96 = 3g + 24

10g = 120

g = 12

Now,

G = 3(12) + 24 = 60

Difference in their present ages

60 - 12 = 48

✅ Correct Answer: 48