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.
$y-0=2\left(x - C_{1}\right)$
$y=2x-2C_{1}\ldots \ldots .\left(i\right)$
Similarly $y=6x-6C_{2}\ldots \ldots .\left(i i\right)$
Both $\left(i\right)$ and $\left(i i\right)$ satisfy $x=40$ and $y=30$
$30=80-2C_{1}\Rightarrow C_{1}=25$
And $30 = 240 - 6 C_{2} \Rightarrow 6 C_{2} = 210 \Rightarrow C_{2} = 35$
Hence, $\left|6 C_{2} - 2 C_{1}\right|=160$