Two numbers are in the ratio $3 : 5$ . If $9$ is subtracted from each number, then they are in the ratio of $12 : 23$ , What is the second numbers.

44

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55

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66

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77

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Solution

The correct option is C $55$
Let the numbers be $3 x$ and $5 x$
According to given condition, $9$ is subtracted from each number and they have ratio $12 : 23$
Therefore, $\frac{3 x - 9}{5 x - 9} = \frac{12}{23}$
$\Rightarrow 69 x - 207 = 60 x - 108$
$\Rightarrow 9 x - 99$
$\Rightarrow x = 11$
Second number $= 5 x = 5 \times 11 = 55$

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