Question

A line is divided into three parts. The first part is two third the length of the second part. The third part is $\frac{1}{2}cm$ shorter than the first part and $2cm$ shorter than the second part. Find the length of the line?

• A. $12cm$
• B. $10cm$
• C. $9cm$
• D. $8cm$

Answer 1

The correct option is B $10cm$

Let the length of the parts be $x,y,z$
As per the question,
$x=\frac{2}{3}y$ ....... $\left(1\right)$

$z=x-\frac{1}{2}$ and $z=y-2$

So, $x-\frac{1}{2}=y-2$
$\Rightarrow 2y=2x+3$ ....... $\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$
$\Rightarrow 2y=2\times \frac{2}{3}y+3$
$\Rightarrow y=\frac{9}{2}$
$\Rightarrow x=\frac{2}{3}\times \frac{9}{2}=3$
$z=y-2=\frac{9}{2}-2=\frac{5}{2}$
So, the length of wire is $=\frac{9}{2}+3+\frac{5}{2}=10cm$