Two trains 125 metres and 115 metres in length, are running towards each other on parallel lines, one at the rate of 33 km/hr and the other at 39 km/hr. How much time (in seconds) will they take to pass each other from the moment they meet?
125 मीटर और 115 मीटर लंबाई की दो गाड़ियाँ समांतर लाइनों पर एक दूसरे की ओर क्रमश: 33 किमी/घंटा और 39 किमी/घंटा की चाल से चल रही है। उन्हें आपस में मिलने के क्षण से एक दूसरे को पार करने में कितना समय लगेगा? (सेकंड में)

Options

A. A)8
B. B)10
C. C)12
D. D)15

Explanation

To solve the problem of how much time the two trains will take to pass each other from the moment they meet, we can follow these steps:

### Step 1: Identify the lengths of the trains
Let:
- Length of the first train (L1) = 125 meters
- Length of the second train (L2) = 115 meters

### Step 2: Identify the speeds of the trains
Let:
- Speed of the first train (S1) = 33 km/hr
- Speed of the second train (S2) = 39 km/hr

### Step 3: Calculate the relative speed of the trains
Since the trains are moving towards each other, their relative speed (SR) is the sum of their speeds:
\[ SR = S1 + S2 = 33 \text{ km/hr} + 39 \text{ km/hr} = 72 \text{ km/hr} \]

### Step 4: Convert the relative speed from km/hr to m/s
To convert km/hr to m/s, we use the conversion factor \( \frac{5}{18} \):
\[ SR = 72 \text{ km/hr} \times \frac{5}{18} = 20 \text{ m/s} \]

### Step 5: Calculate the total distance to be covered
The total distance (D) that needs to be covered for the trains to completely pass each other is the sum of their lengths:
\[ D = L1 + L2 = 125 \text{ m} + 115 \text{ m} = 240 \text{ m} \]

### Step 6: Calculate the time taken to pass each other
Using the formula for time, \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \):
\[ \text{Time} = \frac{D}{SR} = \frac{240 \text{ m}}{20 \text{ m/s}} = 12 \text{ seconds} \]

### Final Answer
The time taken for the two trains to pass each other from the moment they meet is **12 seconds**.

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