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
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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