Question

The velocities of car, a bike and a train are in the ratio 5 : 3 : 8. If a person travels equal distances by a car, a bike and a train, then what would be the ratio of the respective times taken to cover that distance?

• A. 24:40:25
• B. 24:40:05
• C. 24:20: 15
• D. 24:40:15

Answer 1

The Correct Option is D

Finding the Ratio of Time Taken by Car, Bike, and Train

Step 1: Define Variables

Let the total distance to be covered be \( D \). 

Let the speeds of each mode of transport be:

• Car: \( 5x \)
• Bike: \( 3x \)
• Train: \( 8x \)

Step 2: Compute Time Taken

Since time is given by:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

The time taken by each mode is:

• Time by car: \[ \frac{D}{5x} \]
• Time by bike: \[ \frac{D}{3x} \]
• Time by train: \[ \frac{D}{8x} \]

Step 3: Compute the Ratio

\[ \frac{D}{5x} : \frac{D}{3x} : \frac{D}{8x} \]

Canceling \( D/x \) from all terms:

\[ \frac{1}{5} : \frac{1}{3} : \frac{1}{8} \]

Step 4: Convert to Whole Numbers

Find the LCM of denominators \( 5, 3, 8 \), which is 120. Multiply each fraction by 120:

• \( \frac{1}{5} \times 120 = 24 \)
• \( \frac{1}{3} \times 120 = 40 \)
• \( \frac{1}{8} \times 120 = 15 \)

Final Answer:

Thus, the correct ratio of times is 24:40:15 (Option D).