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Four years ago, the age of the mother was 13 times the age of her daughter. Two years hence, the mother's age will be 4 times the daughter's age. After how many years will the mother's age be 3 times that of her daughter?

Four years ago, the age of the mother was 13 times the age of her daughter. Two years hence, the mother's age will be 4 times the daughter's age. After how many years will the mother's age be 3 times that of her daughter? Correct Answer 6

Given:

Four years ago, the age of the mother was 13 times the age of her daughter. 

Two years hence, the mother's age will be 4 times the daughter's age. 

Calculation:

Let the present age of the daughter be Q years.

Four years ago, the age of the daughter = (Q - 4) years

Four years ago, the age of the mother = 13 × (Q - 4)

⇒ (13Q - 52) years

Two years hence,

Age of the daughter = (Q - 4) + 4 + 2 = (Q + 2) years

Age of the mother = (13Q - 52) + 4 + 2 = (13Q - 46) years

According to the question,

(Q + 2) × 4 = (13Q - 46) 

⇒ 4Q + 8 = 13Q - 46

⇒ 13Q - 4Q = 46 + 8

⇒ 9Q = 54

⇒ Q = 54/9

⇒ Q = 6

Now, the present age of the mother = (13Q - 52) + 4

⇒ 13Q - 48

⇒ 13 × 6 - 48

⇒ 30

Let after M years the age of the mother will be three times of her daughter.

According to the question,

(6 + M) × 3 = (30 + M)

⇒ 18 + 3M = 30 + M

⇒ 2M = 30 - 18

⇒ M = 12/2

⇒ M = 6

∴ After 6 years the mother's age will be 3 times that of her daughter.

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