Question

A man covers half of his journey by train at 90 km/hr, one-third of the remainder by bus at 30 km/hr and the rest by cycle at 10 km/hr. The average speed during the entire journey is ______ .

• A. 22.5 km/hr
• B. 28.5 km/hr
• C. 30.0 km/hr
• D. 32.5 km/hr

Answer 1

The Correct Option is A

To find the average speed of the journey, we must first determine the total distance and the total time taken.

Step 1: Assume the total distance is \( D \). 

Step 2: Calculate the distance covered and time taken in each segment of the journey:

1. Distance by train: \(\frac{D}{2}\) at 90 km/hr.
   • Time = \(\frac{\frac{D}{2}}{90} = \frac{D}{180}\) hours.
2. Distance by bus is \(\frac{1}{3}\) of the remainder: \(\frac{1}{3} \times \frac{D}{2} = \frac{D}{6}\) at 30 km/hr.
   • Time = \(\frac{\frac{D}{6}}{30} = \frac{D}{180}\) hours.
3. Distance by cycle: \(D - \frac{D}{2} - \frac{D}{6} = \frac{D}{3}\) at 10 km/hr.
   • Time = \(\frac{\frac{D}{3}}{10} = \frac{D}{30}\) hours.

Step 3: Calculate total time:

\[\text{Total Time} = \frac{D}{180} + \frac{D}{180} + \frac{D}{30} = \frac{4D}{180} = \frac{2D}{90}\]

Step 4: Calculate average speed:

\[\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{D}{\frac{2D}{90}} = 22.5 \, \text{km/hr}\]

The correct answer is 22.5 km/hr.