The distance between two towns is 50km. It is represented on a map by 5cm. Find the scale used

Analyze the question: A real distance of 50 km is shown as 5 cm on a map. We need the scale as a ratio (map : actual) in the same units.

Concept: A scale of 1 : n means 1 cm on the map represents n cm in real life. Both quantities must be in the same unit before you write the ratio.

Solution:

Step 1: Convert 50 km to cm.

• 1 km = 1,000 m = 100,000 cm
• 50 km = 50 × 100,000 = 5,000,000 cm

Step 2: Write the ratio of map distance to actual distance.

• Scale = 5 cm : 5,000,000 cm

Step 3: Divide both sides by 5.

• Scale = 1 : 1,000,000

Checking against the options: 1 : 1,000,000 is option A. Option B (1 : 500,000) would make 5 cm represent only 25 km, so it is wrong.

Answer: A. 1 : 1,000,000

Tip: Remember that 1 km = 100,000 cm. Convert the real distance to cm first, then divide both sides by the map distance. A common mistake is leaving the ratio in mixed units (km and cm), so always check your units before writing the scale.