Question

If the points $A,B,C,D$ are collinear and $C,D$ divide $AB$ in the ratios $2:3,-2:3$ respectively, then the ratio in which $A$ divides $CD$ is

• A. $5:1$
• B. $2:3$
• C. $3:2$
• D. $1:5$

Answer 1

The correct option is D $1:5$

$C$ divide $AB$ in the ratio of $2:3$

$\Rightarrow AC=2x,CB=3x$

$D$ divide $AB$ in the ratio of $-2:3$

$\Rightarrow DA=2y,DB=3y$

$\Rightarrow AB=DB-DA=y$

$\Rightarrow 5x=y\Rightarrow x=\frac{y}{5}$

$\Rightarrow CA:AD=2x:2y=\frac{x}{y}=\frac{\frac{y}{5}}{y}=\frac{1}{5}$

$\Rightarrow$ $A$ divides $CD$ in the ratio $1:5$