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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