Question : The ratio of the present ages of the two boys is $3:4$. After 3 years, the ratio of their ages will be $4:5$. The ratio of their ages after 21 years will be:
Option 1: $14:17$
Option 2: $17:19$
Option 3: $11:12$
Option 4: $10:11$
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Correct Answer: $10:11$
Solution :
Let the present age of boys be $3x$ years and $4x$ years respectively.
According to the given condition:
After 3 years,
$⇒\frac{3x+3}{4x+3}=\frac{4}{5}$
$⇒ 15x+15 = 16x+12$
$\therefore x = 3$
So, the present age of boys is 9 years and 12 years respectively.
Therefore, the ratio of their age after 21 years is $=\frac{9+21}{12+21}$
$=\frac{30}{33}$
$=\frac{10}{11}$
Thus, the ratio of the age after 21 years is $10:11$.
Hence, the correct answer is $10:11$.
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