Question

A line with gradient $2$ intersects a line with gradient $6$ at the point $\left(40,30\right).$ The distance between $y$ -intercepts of these lines is

• A. $160$
• B. $180$
• C. $108$
• D. $120$

Answer 1

Answer: (A)

Let $C_1$ and $C_2$ be the $x$ -intercept of line with slope $2$ and $6$ respectively.
$y-0=2\left(x-C_1\right)$
$y=2x-2C_1\dots \dots .\left(i\right)$
Similarly $y=6x-6C_2\dots \dots .\left(ii\right)$
Both $\left(i\right)$ and $\left(ii\right)$ satisfy $x=40$ and $y=30$
$30=80-2C_1\Rightarrow C_1=25$
And $30=240-6C_2\Rightarrow 6C_2=210\Rightarrow C_2=35$
Hence, $\left|6C_2-2C_1\right|=160$