$$\frac{1}{{10}}$$ of a pole is coloured red, $$\frac{1}{{20}}$$ white, $$\frac{1}{{30}}$$ blue, $$\frac{1}{{40}}$$ black, $$\frac{1}{{50}}$$ violet, $$\frac{1}{{60}}$$ yellow and the rest is green. If the length of the green portion of the pole is 12.08 metres, then the length of the pole is = ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Green portion}} \cr & = \left[ {1 - \left( {\frac{1}{{10}} + \frac{1}{{20}} + \frac{1}{{30}} + \frac{1}{{40}} + \frac{1}{{50}} + \frac{1}{{60}}} \right)} \right] \cr & = \left[ {1 - \frac{1}{{10}}\left( {1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}} \right)} \right] \cr & = 1 - \frac{1}{{10}} \times \frac{{147}}{{60}} \cr & = 1 - \frac{{147}}{{600}} \cr & = \frac{{453}}{{600}} \cr & {\text{let the length of the pole be }}x{\text{ metres}} \cr & {\text{Then, }}\frac{{453}}{{600}}x = 12.08 \cr & \Leftrightarrow x = \left( {\frac{{12.08 \times 600}}{{453}}} \right) = 16 \cr} $$