On a scale of map, 0.6 cm represents 6.6 km. If the distance between the points on the map is 80.5 cm, the actual distance between these points is

### Concept & Scaling in Maps Map scales represent a direct ratio between the distance on the map and the actual distance on the ground. $$ \text{Actual Distance} = \text{Map Distance} \times \left( \frac{\text{Actual Scale Reference}}{\text{Map Scale Reference}} \right) $$ ### Step-by-Step Solution * Given: Map scale is 0.6 cm = 6.6 km. * Calculate the actual distance represented by 1 cm on the map: $\frac{6.6}{0.6} = 11$ km. * Given map distance between points = 80.5 cm. * Actual distance = $80.5 \times 11 = 885.5$ km. ### Exam Strategy & Shortcut Multiply $80.5 \times 11$ quickly using the 11-multiplication trick. Split the numbers: $805 \times 11$. $8 | 8+0 | 0+5 | 5 \rightarrow 8855$. Add the one decimal place back to get $885.5$. ### Common Pitfall Setting up the ratio upside down or incorrectly dealing with the decimals in $0.6$ and $6.6$, which could lead to answers off by a factor of 10. ### Final Answer Therefore, the correct answer is **885.5 km**.