Two stations A and B are 110 kms apart on a straight line. One train starts fromA at 7 A.M. and travels towards B at 20 km/hr. speed. Another train starts from B at 8 A.M. and travels towards A at 25 km/hr. speed. At what time will they meet?

Options

A. 9 A.M.
B. 10 A.M.
C. 11 A.M.
D. 12 A.M.

Answer

To solve the problem of when the two trains will meet, we can follow these steps:

### Step 1: Determine the distance covered by the first train before the second train starts.
- The first train leaves station A at 7 A.M. and travels at a speed of 20 km/hr.
- The second train leaves station B at 8 A.M.
- Therefore, the first train travels for 1 hour before the second train starts.

**Distance covered by the first train in 1 hour:**
\[ \text{Distance} = \text{Speed} \times \text{Time} = 20 \text{ km/hr} \times 1 \text{ hr} = 20 \text{ km} \]

### Step 2: Calculate the remaining distance between the two trains when the second train starts.
- The total distance between stations A and B is 110 km.
- After 1 hour, the first train has covered 20 km, so the remaining distance is:
\[ \text{Remaining distance} = 110 \text{ km} - 20 \text{ km} = 90 \text{ km} \]

### Step 3: Determine the relative speed of the two trains.
- The first train travels at 20 km/hr and the second train travels at 25 km/hr.
- Since they are moving towards each other, we can add their speeds to find the relative speed:
\[ \text{Relative speed} = 20 \text{ km/hr} + 25 \text{ km/hr} = 45 \text{ km/hr} \]

### Step 4: Calculate the time taken for the two trains to meet.
- We can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- The distance they need to cover to meet is 90 km, and their relative speed is 45 km/hr:
\[ \text{Time} = \frac{90 \text{ km}}{45 \text{ km/hr}} = 2 \text{ hours} \]

### Step 5: Determine the time of meeting.
- The second train starts at 8 A.M. and they will meet after 2 hours:
\[ \text{Meeting time} = 8 \text{ A.M.} + 2 \text{ hours} = 10 \text{ A.M.} \]

### Final Answer:
The two trains will meet at **10 A.M.**.

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