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Eight years ago, Maria’s age was equal to the sum of the present ages of her only son and only daughter. Ten years hence, the respective ratio between the ages of her daughter and her son that time will be 6 : 5. If Maria ‘s husband is 8 years elder to her and his present age is four times the present age of their son, what is the present age of Maria’s daughter?

Eight years ago, Maria’s age was equal to the sum of the present ages of her only son and only daughter. Ten years hence, the respective ratio between the ages of her daughter and her son that time will be 6 : 5. If Maria ‘s husband is 8 years elder to her and his present age is four times the present age of their son, what is the present age of Maria’s daughter? Correct Answer 14 years

Calculation

Let present age of her son be x

⇒ Present age of Maria’s husband = 4x

⇒ Present age of Maria = 4x – 8

Eight years ago, Maria’s age = 4x – 16

⇒ Present age of her daughter = (4x – 16) – x = 3x – 16

After 10 years age of her daughter = 3x – 6

After 10 years age of her son = x + 10

Now according to question,

(3x – 6) : (x + 10) = 6 : 5

⇒ 15x – 30 = 6x + 60

⇒ 9x = 90

⇒ x = 10

∴ Present age of her daughter = (3 × 10 – 16) = 14 years

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