The ratio between the speeds of two trains is, 2 : 5. If the first train runs 350 km in 5 h. then the difference between the speeds (in km/h) of both the trains is :

Options

A. 75
B. 180
C. 65
D. 105

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Determine the speed of the first train (Train A)
Given that Train A runs a distance of 350 km in 5 hours, we can calculate its speed using the formula:

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

Substituting the values:

\[ \text{Speed of Train A} = \frac{350 \text{ km}}{5 \text{ h}} = 70 \text{ km/h} \]

### Step 2: Understand the ratio of speeds
The ratio of the speeds of Train A and Train B is given as 2:5. This means:

\[ \text{Speed of Train A} : \text{Speed of Train B} = 2 : 5 \]

Let’s denote the speed of Train A as \( 2x \) and the speed of Train B as \( 5x \).

### Step 3: Set up the equation for Train A's speed
From Step 1, we know that the speed of Train A is 70 km/h. Therefore, we can set up the equation:

\[ 2x = 70 \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides of the equation by 2:

\[ x = \frac{70}{2} = 35 \]

### Step 5: Calculate the speed of Train B
Now that we have \( x \), we can find the speed of Train B:

\[ \text{Speed of Train B} = 5x = 5 \times 35 = 175 \text{ km/h} \]

### Step 6: Find the difference between the speeds of both trains
Now, we can find the difference between the speeds of Train B and Train A:

\[ \text{Difference} = \text{Speed of Train B} - \text{Speed of Train A} = 175 \text{ km/h} - 70 \text{ km/h} = 105 \text{ km/h} \]

### Final Answer
The difference between the speeds of both trains is **105 km/h**.

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