A man performs $\frac{3}{5}$ of the total journey by rail, $\frac{7}{20}$ by bus and the remaining $6.5\text{ km}$ on foot. His total journey is

### Concept & Logic This is a fraction-based distance problem. The entire journey represents a whole ($1$). The remaining fractional part corresponds to the remaining absolute distance. ### Step-by-Step Solution * **Given:** * Fraction by rail = $\frac{3}{5}$ * Fraction by bus = $\frac{7}{20}$ * Distance on foot = $6.5$ km * **Calculation:** * Let the total journey be $x$ km. * Fraction of journey covered = $\frac{3}{5} + \frac{7}{20}$ * To add these, find a common denominator ($20$): $\frac{12}{20} + \frac{7}{20} = \frac{19}{20}$ * Remaining fraction of the journey = $1 - \frac{19}{20} = \frac{1}{20}$ * This remaining fraction equals the distance travelled on foot: $$ \frac{1}{20} \text{ of } x = 6.5 $$ $$ x = 6.5 \times 20 = 130\text{ km} $$ ### Exam Strategy & Shortcut Work purely with fractions. Since the parts sum to $\frac{19}{20}$, the remaining $1$ part out of $20$ is $6.5$ km. Thus, $20$ parts = $6.5 \times 20 = 130$ km. This mental math avoids algebra entirely. ### Common Pitfall Making arithmetic errors when finding a common denominator for the fractions. ### Final Answer Therefore, the correct answer is **130 km**.