A passenger train leaves a station at a certain time and at a fixed speed. After, 10 hours, a superfast train leaves the same station and in the same direction moving at a uniform speed of 90 kmph. The train catches the passenger train in 5 hours. Find the speed of passenger train.

Options

A. A)30 kmph
B. B)25 kmph
C. C)28kmph
D. D)32 kmph

Answer

To solve the problem, we will follow these steps:

### Step 1: Define Variables
Let the speed of the passenger train be \( V_P \) km/h. The speed of the superfast train is given as \( 90 \) km/h.

### Step 2: Calculate the Time Traveled by Each Train
- The passenger train travels for a total of \( 10 + 5 = 15 \) hours before being caught by the superfast train.
- The superfast train travels for \( 5 \) hours.

### Step 3: Set Up the Distance Equation
The distance traveled by both trains when the superfast train catches up with the passenger train is the same. We can express the distances as:
- Distance traveled by the passenger train:
\[ \text{Distance}_P = V_P \times 15 \]
- Distance traveled by the superfast train:
\[ \text{Distance}_{SF} = 90 \times 5 = 450 \text{ km} \]

### Step 4: Set the Distances Equal
Since both distances are equal when the superfast train catches the passenger train, we can set up the equation:
\[ V_P \times 15 = 450 \]

### Step 5: Solve for \( V_P \)
To find the speed of the passenger train, rearrange the equation:
\[ V_P = \frac{450}{15} \]
Calculating this gives:
\[ V_P = 30 \text{ km/h} \]

### Conclusion
The speed of the passenger train is \( 30 \) km/h.

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