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
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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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