Question : The ratio of the ages of two boys is 5 : 6. After two years, the ratio will be 7 : 8. Determine the ratio of their ages after 12 years.
Option 1: $\frac{22}{24}$
Option 2: $\frac{15}{16}$
Option 3: $\frac{17}{18}$
Option 4: $\frac{11}{12}$
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Correct Answer: $\frac{17}{18}$
Solution : Given: The ratio of the age of two boys is 5 : 6. After two years, the ratio will be 7 : 8. Let the age of two boys be $5x$ years and $6x$ years respectively. As per conditions, we have: $\frac{5x+2}{6x+2}=\frac{7}{8}$ ⇒ $40x+16=42x+14$ ⇒ $2x=2$ ⇒ $x=1$ Required ratio after 12 years, = $(5x+12):(6x+12)$ = (5 + 12) : (6 + 12) = 17 : 18 Hence, the correct answer is $\frac{17}{18}$.
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