Question : The ratio of the present age of two girls is 3 : 4. After two years, the ratio will be 7 : 9. Which of the following statement(s) is/are correct?
I. The ratio of their ages after 10 years is 6 : 7.
II. The ratio of their ages after 12 years is 6 : 7.
Option 1: Both I and II
Option 2: Only II
Option 3: Neither I nor II
Option 4: Only I
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Correct Answer: Only II
Solution :
Let the ages of the two girls be $3x$ and $4x$ years respectively.
According to the question,
$\frac{3x+2}{4x+2}=\frac{7}{9}$
⇒ $27x+18=28x+14$
⇒ $x=4$
Their ages are 12 years and 16 years respectively.
Ratio of their ages after 10 years = (12 + 10) : (16 + 10) = 22 : 26 = 11 : 13
Ratio of their ages after 12 years = (12 + 12) : (16 + 12) = 24 : 28 = 6 : 7
Hence, the correct answer is Only II.
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