From stations M and N ,two trains start moving towards each other at speed 125km/h and 75k m/h,respectively .When the two trains meet each other ,it is found that one train covers 50 km more than an other. Find the distance betweenMandN.

Options

A. a. 190km
B. b. 200km
C. c. 145km
D. d. 225km

Answer

To solve the problem step by step, we will use the information given about the two trains and their speeds.

### Step 1: Define Variables
Let:
- \( d_1 \) = distance covered by the first train (speed = 125 km/h)
- \( d_2 \) = distance covered by the second train (speed = 75 km/h)

According to the problem, when the two trains meet, one train covers 50 km more than the other. Therefore, we can express this relationship as:
\[ d_1 = d_2 + 50 \]

### Step 2: Relate Distances to Time
Since both trains start at the same time and meet at the same time, we can express the distances in terms of time \( t \):
- For the first train:
\[ d_1 = 125t \]
- For the second train:
\[ d_2 = 75t \]

### Step 3: Substitute the Distances
Now we can substitute \( d_1 \) and \( d_2 \) into the equation we established in Step 1:
\[ 125t = 75t + 50 \]

### Step 4: Solve for Time \( t \)
Now, we will solve for \( t \):
1. Rearranging the equation:
\[ 125t - 75t = 50 \]
\[ 50t = 50 \]
2. Dividing both sides by 50:
\[ t = 1 \text{ hour} \]

### Step 5: Calculate Distances
Now that we have the time, we can find the distances covered by each train:
- Distance covered by the first train:
\[ d_1 = 125t = 125 \times 1 = 125 \text{ km} \]
- Distance covered by the second train:
\[ d_2 = 75t = 75 \times 1 = 75 \text{ km} \]

### Step 6: Find Total Distance Between M and N
The total distance between stations M and N is the sum of the distances covered by both trains:
\[ \text{Total Distance} = d_1 + d_2 = 125 \text{ km} + 75 \text{ km} = 200 \text{ km} \]

### Final Answer
The distance between stations M and N is **200 km**.

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