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The length of a rubber cord is $l_{1}$ meters when the tension in its is 4N and $l_{2}$ meters when the tension is 5N. Then the length in meters when the tension is 9N is ....

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$5 l_{1} - 3 l_{1}$

$5 l_{1} - 2 l_{1}$

$5 l_{2} - 4 l_{1}$

$4 l_{2} - 5 l_{1}$

answer is C.

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Detailed Solution

$\begin{matrix} l_{1} - l α 4 \\ l_{2} - l α 5 \\ l_{3} - l α 9 \end{matrix} \frac{l_{1} - 1}{l_{2} - 1} = \frac{4}{2} \Rightarrow l = 5 l_{1} - 4 l_{2}$

$\frac{l_{1} - l}{l_{3} - l} = \frac{4}{9} \Rightarrow l_{3} = 5 l_{2} - 4 l_{1}$

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