How many pieces of 85 cm length can be cut from a rod 42.5 metres long?

### Concept & Strategy Before dividing a total length by a piece length, you must standardize the units. Both values must be in either meters or centimeters. $$Number\ of\ Pieces = \frac{Total\ Length\ (in\ cm)}{Length\ per\ Piece\ (in\ cm)}$$ ### Step-by-Step Solution * **Given:** * Rod length = 42.5 meters * Piece length = 85 cm * **Calculation:** 1. Convert the total rod length from meters to centimeters (since 1 meter = 100 cm): $42.5 \times 100 = 4250$ cm. 2. Divide the total length by the length of a single piece to find the count: $4250 / 85 = 50$ pieces. 3. Look at the options provided: (a) 30, (b) 40, (c) 60. Since 50 is not listed, the correct choice is 'None of these'. ### Exam Strategy & Shortcut Look at the numerical relationship between the significant digits. $85$ is exactly double $42.5$. So, $42.5 / 85$ is $0.5$. Because of the meter-to-centimeter conversion factor of 100, you just multiply $0.5 \times 100 = 50$. Since 50 isn't an option, select 'None of these' instantly. ### Common Pitfall The primary mistake here is failing to convert units, leading students to divide $42.5$ by $85$ directly and getting $0.5$, or multiplying incorrectly and landing on a distractor. Always harmonize units before operating on them. ### Final Answer **Therefore, the correct answer is None of these.**