Let ABC be a triangle. If P is a point such that AP divides BC in the ratio 2 : 3, BP divides CA in the ratio 3 : 5 then the ratio in which CP divides AB is

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$5 : 2$

$2 : 5$

$2 : - 5$

$5 : - 2$

answer is C.

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Detailed Solution

Let BD : DC = 2 : 3 and CE : AE = 3 : 5

From ceva’s theorem

$\begin{array}{l} \frac{B D}{D C} . \frac{C E}{E A} . \frac{A F}{F B} = 1 \\ \Rightarrow \frac{2}{3} . \frac{3}{5} . \frac{A F}{F B} = 1 \Rightarrow \frac{A F}{F B} = \frac{5}{2} \end{array}$

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