Question

In $\Delta ABC$, $E$ divides AB in the ratio $3:1$ and F divides BC in the ratio $3:2$, then the ratio of areas of $\Delta BEF$ and $\Delta ABC$ is

• A. $3:5$
• B. $3:10$
• C. $1:5$
• D. $3:20$

Answer 1

The correct option is D $3:20$

Let Area of $\Delta BEF=x$
$\therefore$ Area of $\Delta AFE=3x$
Let Area of $\Delta ABF=3y$
$\therefore$ Area of $\Delta CAF=2y$
Area $\Delta ABC=$ Area $\Delta BEF+$ Area $\Delta AEF$
$3y=x+3x$ (i)
$3y=4x$
$\frac{3}{4}=\frac{x}{y}$
$\frac{Area\Delta BEF}{Area\Delta ABC}=\frac{x}{y}=\frac{1}{5}\times \frac{3}{4}=\frac{3}{20}$