$\frac{1}{10}$ 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

### Concept & Strategy The whole pole represents 1 entire unit. The sum of all the coloured fractions subtracted from 1 will give the fraction representing the green portion. Equating this final fraction to the actual length given (12.08 m) allows you to solve for the total length of the pole. ### Step-by-Step Solution * **Add all the given fractions:** $$\text{Sum} = \frac{1}{10} + \frac{1}{20} + \frac{1}{30} + \frac{1}{40} + \frac{1}{50} + \frac{1}{60}$$ * **Find the Least Common Multiple (LCM) of the denominators:** The LCM of 10, 20, 30, 40, 50, 60 is 600. * **Convert each fraction:** $$\text{Sum} = \frac{60 + 30 + 20 + 15 + 12 + 10}{600} = \frac{147}{600}$$ * **Find the remaining (green) fraction:** $$\text{Green Fraction} = 1 - \frac{147}{600} = \frac{453}{600}$$ * **Calculate the total length:** Let the total length be $x$. $$\frac{453}{600} \times x = 12.08$$ $$x = 12.08 \times \frac{600}{453}$$ $$x = \frac{1208 \times 6}{453}$$ $$x = \frac{7248}{453} = 16 \text{ m}$$ ### Exam Strategy & Shortcut When facing a messy division like $7248 \div 453$, use unit digits to quickly estimate. The last digit of 453 is 3. We need a multiplier that gives 8 in the unit digit ($3 \times 6 = 18$). Looking at the options (16, 18, 20, 30), only 16 ends in a 6. A quick check of $450 \times 16$ confirms it is around 7200. ### Common Pitfall Making arithmetic mistakes while calculating the LCM for six different numbers. If you miss a factor, the common denominator will be wrong, drastically changing the remainder fraction and the final calculation. ### Final Answer **Therefore, the correct answer is 16 m.**