$$\frac{1}{{10}}$$ 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 rest is violet. If length of violet part of rod is 12.08 mtr, n length of rod is -

Let the total length of rod is 1 unit
According to question,
$$ \Rightarrow 1 - \frac{1}{{10}} - \frac{1}{{20}} - \frac{1}{{30}} - \frac{1}{{40}} - \frac{1}{{50}}$$       $$ - \frac{1}{{60}}$$

$$ \Rightarrow \frac{{600 - 60 - 30 - 20 - 15 - 12 - 10}}{{600}}$$
$$\eqalign{ & \Rightarrow \frac{{453 \leftarrow {\text{ Violet part}}}}{{600 \leftarrow {\text{ Total part}}}} \cr & 453{\text{ part }} \to {\text{ 12}}{\text{.08 mtr}} \cr & {\text{1 part }} \to \,\,\,\,\,\,\,\,\frac{{12.08}}{{453}} \cr & 600{\text{ part }} \to \frac{{12.08}}{{453}} \times 600 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 16{\text{mtr}} \cr} $$
So total length of rod is 16 metres.