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 are violet. If the lenght of the violet portion is 12.08 m, then what is the lenght of the rod?

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

Answer 1

Answer: (A)

$16$m

part of the rod that is coloured violet
$=1-(\frac{1}{10}+\frac{1}{20}+\frac{1}{30}+\frac{1}{40}+\frac{1}{50}+\frac{1}{60})$
$=1-\frac{60+30+20+15+12+10}{600}$
$=1-\frac{147}{600}=1-\frac{49}{200}=\frac{151}{200}$
Given $\frac{151}{200}$ of the whole = 12.08 m
$\Rightarrow whole=\frac{12.08\times 200}{151}m=\frac{2416}{151}m=16m$