If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is

### Concept & Equating Time When a person travels for the same unknown duration ($t$) but at two different speeds, resulting in two different distances, we can equate the time to find the actual distance. $$Time = \frac{Distance}{Speed}$$ ### Step-by-Step Solution 1. Let the actual distance travelled by the person be $x$ km. 2. The actual speed of the person is $10$ km/hr. The time taken is $\frac{x}{10}$ hours. 3. If he walks at $14$ km/hr, the new distance covered is $(x + 20)$ km. 4. The time taken in this hypothetical scenario is $\frac{x + 20}{14}$ hours. 5. Since the time spent walking in both cases is the same, we equate the two time expressions: $$\frac{x}{10} = \frac{x + 20}{14}$$ 6. Cross-multiply to solve for $x$: $$14x = 10(x + 20)$$ $$14x = 10x + 200$$ $$14x - 10x = 200$$ $$4x = 200$$ $$x = 50 \text{ km}$$ ### Exam Strategy & Shortcut Think about relative change. The increase in speed is $4$ km/hr ($14 - 10$). This $4$ km/hr extra speed causes an extra $20$ km to be covered. Therefore, the time he walked is $\frac{20 \text{ km}}{4 \text{ km/hr}} = 5 \text{ hours}$. The actual distance travelled at the actual speed ($10$ km/hr) in those $5$ hours is $10 \times 5 = 50$ km. ### Common Pitfall Students often calculate the time ($5$ hours) and then mistakenly multiply it by the hypothetical speed ($14$ km/hr) yielding $70$ km, forgetting the question asks for the *actual* distance travelled. ### Final Answer Therefore, the correct answer is **50 km**.