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.
Option 1: 45 and 15
Option 2: 40 and 10
Option 3: 42 and 12
Option 4: 50 and 20
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Correct Answer: 42 and 12
Solution : Let the present age of the mother be $x$ and the age of the daughter be $y$. According to the question, $x-7 = 7(y-7)$ ⇒ $x-7 = 7y - 49$ ⇒ $x-7y = -42$ Also after 3 years, $x+3 = 3(y+3)$ ⇒ $x-3y = 6$ Solving the equations simultaneously we get, $y=12$ and $x = 42$ Hence, the correct answer is 42 and 12.
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