Question : The sum of the ages of the mother and her daughter is 60 years. 12 years ago, the mother was eight times as old as her daughter. How old is the daughter at present?
Option 1: 20 years
Option 2: 28 years
Option 3: 16 years
Option 4: 12 years
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Correct Answer: 16 years
Solution : Let the current age of the mother be $x$ and the daughter be $y$. The sum of their current ages is $60$ years, ⇒ $x+ y = 60$...(i) $12$ years ago, the mother was eight times as old as the daughter. ⇒ $x - 12 = 8(y - 12)$...(ii) Solving equations (i) and (ii), $(60 - y) - 12 = 8(y - 12)$ ⇒ $48 - y = 8y - 96$ ⇒ $y = \frac{48 + 96}{9} = 16$ Hence, the correct answer is 16 years.
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Question : Mother told her daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be". Find the present ages of the mother and the daughter, respectively.
Question : Direction: A mother is five times older than her daughter. After 5 years, she would be 3 times older than her daughter. Find the mother's present age.
Question : Eight years ago, the ratio of the ages of A and B was 5 : 4. The ratio of their present ages is 6 : 5. What will be the sum (in years) of the ages of A and B 7 years from now?
Question : The ratio of the present ages of R and S is 11 : 17. 11 years ago, the ratio of their ages was 11 : 20. What is R's present age (in years)?
Question : The present age of Rahim is five times the present age of his daughter, Savita. Seven years from now, Rahim will be three times as old as Savita. What is the present age (in years) of Rahim?
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