Question

A man performs 2/15 of the total journey by rail, 9/20 by bus and remaining 10 km on the cycle. His total journey is

• A. 31.2 km
• B. 38.4 km
• C. 32.8 km
• D. 24 km

Hint:

Remaining fraction $= 1 - (\frac{2}{15} + \frac{9}{20}) = \frac{5}{12}$. Since $\frac{5}{12} x = 10\text{ km} \implies x = 24\text{ km}$.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The sum of all fractional segments of the journey equals the total journey distance $x$.

Step 2: Key Formula or Approach:
Fraction of journey covered by rail and bus:
\[\text{Fraction covered} = \frac{2}{15} + \frac{9}{20} = \frac{8 + 27}{60} = \frac{35}{60} = \frac{7}{12}\] Remaining fraction covered by cycle:
\[\text{Remaining fraction} = 1 - \frac{7}{12} = \frac{5}{12}\]

Step 3: Detailed Explanation:
Equating the remaining fraction to $10\,\text{km}$:
\[\frac{5}{12} x = 10 \implies x = 10 \times \frac{12}{5} = 24\,\text{km}\]

Step 4: Final Answer:
Therefore, the total journey is 24 km.