Question

$\frac{1}{10}$ of a rod is coloured red, $\frac{1}{20}$ orange, $\frac{1}{30}$ yellow, $\frac{1}{40}$ green, $\frac{1}{50}$ blue, $\frac{1}{60}$ black and the rest violet. If the length of the violet portion is $12.06m$, then what is the length of the rod?

• A. $16m$
• B. $18m$
• C. $20m$
• D. $30m$

Answer 1

The correct option is A $16m$

Let the length of the rod be $x$ $m$
$\therefore$ Length of the rod coloured be red$=\frac{1}{10}$ $x$ $m$
$\therefore$ Length of the rod coloured be orange$=\frac{1}{20}$ $x$ $m$
Length of the rod coloured be yellow$=\frac{1}{30}$ $x$ $m$
Length of the rod coloured be green$=\frac{1}{40}$ $x$ $m$
Length of the rod coloured be blue$=\frac{1}{50}$ $x$ $m$
Length of the rod coloured be black$=\frac{1}{60}$ $x$ $m$
Length of the rod coloured be violet$=12.08m$
$\therefore$ According to question
$\frac{1}{10}x+\frac{1}{20}x+\frac{1}{30}x+\frac{1}{40}x+\frac{1}{50}x+12.08=x$
$\Rightarrow x-\frac{49}{200}x=12.08\Rightarrow \frac{151}{200}x=12.08\Rightarrow x=16$
$\therefore$ Length of the rod $=16m$