Question : Directions: The mother was three times the age of her daughter five years ago. After five years, the mother will be twice as old as her daughter. How old is the daughter today?
Option 1: 5 years
Option 2: 10 years
Option 3: 15 years
Option 4: 20 years
Correct Answer: 15 years
Solution : Let the daughter's present age be A years.
Five years ago, the daughter's age = (A – 5) years
Her mother's age was three times the age of her daughter = 3 × (A – 5) = (3A – 15) years
So, Mother's present age = (3A – 15) + 5 = (3A – 10) years
After 5 years, Daughter's age = (A + 5) years, and her mother's age = (3A – 10) + 5 = (3A – 5) years
Also, as per the given statement, after five years, the mother will be twice as old as her daughter,
⇒ 3A – 5 = 2 × (A + 5)
⇒ 3A – 5 = 2A + 10
⇒ 3A – 2A = 10 + 5
⇒ A = 15 years
So, the present age of the daughter is 15 years. Hence, the third option is correct.
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