A spider climbed $62\frac{1}{2}\%$ of the height of the pole in one hour and in the next hour it covered $12\frac{1}{2}\%$ of the remaining height. If the height of the pole is 192 m, then distance climbed in second hour is

### Concept & Strategy When dealing with complex percentage values like $62.5\%$ and $12.5\%$, converting them instantly into their fractional equivalents drastically simplifies the calculation. $$62\frac{1}{2}\% = \frac{5}{8}$$ $$12\frac{1}{2}\% = \frac{1}{8}$$ ### Step-by-Step Solution * **Total height** of the pole is given as 192 m. * **First hour climb:** The spider climbs $\frac{5}{8}$ of the total height. * **Remaining height:** If $\frac{5}{8}$ is climbed, the remaining distance is $1 - \frac{5}{8} = \frac{3}{8}$ of the total height. $$\text{Remaining} = \frac{3}{8} \times 192 = 3 \times 24 = 72 \text{ m}$$ * **Second hour climb:** The spider covers $12\frac{1}{2}\%$ (or $\frac{1}{8}$) of this *remaining* height. $$\text{Distance in 2nd hour} = \frac{1}{8} \times 72 = 9 \text{ m}$$ ### Exam Strategy & Shortcut Use a chained fraction multiplication for maximum speed. You only care about the remaining portion after the first hour, and the portion climbed in the second hour. Distance = $\text{Total} \times \text{Remaining Fraction} \times \text{Second Climb Fraction}$ Distance = $192 \times \frac{3}{8} \times \frac{1}{8}$ Distance = $192 \times \frac{3}{64} = 3 \times 3 = 9$. ### Common Pitfall The most frequent mistake is calculating $12.5\%$ of the **total** height (192 m) instead of the **remaining** height (72 m). Always underline the word "remaining" in percentage problems. ### Final Answer **Therefore, the correct answer is 9 m.**