A point $C$ divides a line segment $A B$ in the ratio $5 : 6$ . The ratio of lengths $A B : B C$ is ______.

$5 : 11$

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$6 : 11$

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$11 : 6$

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$11 : 5$

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Solution

The correct option is C
$11 : 6$

Given $A C : B C = 5 : 6$ .
$\Rightarrow \frac{A C}{B C} = \frac{5}{6}$

We already know that, $A B = A C + B C .$

Then,
$\frac{A B}{B C} = \frac{A C + B C}{B C} = \frac{A C}{B C} + 1 = \frac{5}{6} + 1 = \frac{11}{6}$

So, ratio of $A B : B C = 11 : 6$ .

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