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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Question : Directions: The total age of a mother and her daughter is 60 years. The difference between their ages is 30 years. Find out the age of the mother.
Option 1: 40 years
Option 2: 45 years
Option 3: 50 years
Option 4: 55 years
Question : Directions: A father is 5 times as old as his son. His son is 6 years old. After how many years, will the father be 4 times as old as his son?
Option 2: 6 years
Option 3: 4 years
Option 4: 2 years
Option 1: 55 years
Option 2: 40 years
Option 3: 45 years
Option 4: 50 years
Question : Four years ago, Shyam's age was $\frac{3}{4}$th times that of Ram. Four years hence, Shyam's age will be $\frac{5}{6}$th times that of Ram. What is the present age of Shyam?
Option 1: 24 years
Option 2: 20 years
Option 3: 16 years
Option 4: 15 years
Question : Directions: The age of the father is twice that of the elder son. After ten years, the age of the father will be three times that of the younger son. If the difference in ages of the two sons is 15 years, the age of the father is?
Option 1: 70 years
Option 2: 55 years
Option 4: 60 years
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