Train A took 30 minute to covera distance of 50 km. If the speed oftrain B is 40% faster than train A, then the ratio of the respective speed of the both train is:

Options

A. `5 : 3`
B. `3 : 5`
C. `7 : 5`
D. `5 : 7`

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the speed of Train A
- **Distance covered by Train A** = 50 km
- **Time taken by Train A** = 30 minutes

First, we need to convert the time from minutes to hours:
\[ \text{Time in hours} = \frac{30 \text{ minutes}}{60} = 0.5 \text{ hours} \]

Now, we can calculate the speed of Train A using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{50 \text{ km}}{0.5 \text{ hours}} = 100 \text{ km/h} \]

### Step 2: Calculate the speed of Train B
- The speed of Train B is 40% faster than Train A.

To find the speed of Train B:
\[ \text{Speed of Train B} = \text{Speed of Train A} + 40\% \text{ of Speed of Train A} \]
\[ = 100 \text{ km/h} + 0.4 \times 100 \text{ km/h} = 100 \text{ km/h} + 40 \text{ km/h} = 140 \text{ km/h} \]

### Step 3: Calculate the ratio of the speeds of Train A and Train B
Now, we will find the ratio of the speeds of Train A to Train B:
\[ \text{Ratio} = \frac{\text{Speed of Train A}}{\text{Speed of Train B}} = \frac{100 \text{ km/h}}{140 \text{ km/h}} = \frac{100}{140} = \frac{5}{7} \]

### Conclusion
Thus, the ratio of the respective speeds of Train A and Train B is:
\[ \text{Ratio} = 5 : 7 \]

### Final Answer
The correct answer is **5 is to 7**.

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