The distance between two cities A and B is 330km. A train starts from A at 8 a.m. and travels towards B at 60km/hr. Another train starts from B at 9a.m and travels towards A at 75 km/hr. At what time do they meet?

Options

A. 10 a.m
B. 10:30 a.m
C. 11 a.m
D. 11:30 a.m

Answer

To solve the problem step by step, we need to calculate the time at which the two trains meet.

### Step 1: Calculate the distance covered by the first train before the second train starts.
- The first train leaves city A at 8 a.m. and travels at a speed of 60 km/hr.
- The second train leaves city B at 9 a.m.
- Therefore, the first train travels for 1 hour before the second train starts.

**Distance covered by the first train in 1 hour:**
\[ \text{Distance} = \text{Speed} \times \text{Time} = 60 \, \text{km/hr} \times 1 \, \text{hr} = 60 \, \text{km} \]

### Step 2: Calculate the remaining distance between the two trains after the first train has traveled.
- The total distance between A and B is 330 km.
- After the first train has traveled 60 km, the remaining distance is:
\[ \text{Remaining distance} = 330 \, \text{km} - 60 \, \text{km} = 270 \, \text{km} \]

### Step 3: Calculate the combined speed of both trains.
- The speed of the first train is 60 km/hr and the speed of the second train is 75 km/hr.
- Therefore, the combined speed of both trains is:
\[ \text{Combined speed} = 60 \, \text{km/hr} + 75 \, \text{km/hr} = 135 \, \text{km/hr} \]

### Step 4: Calculate the time taken for the two trains to meet after 9 a.m.
- We need to find the time taken to cover the remaining distance of 270 km at a combined speed of 135 km/hr.
- Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{270 \, \text{km}}{135 \, \text{km/hr}} = 2 \, \text{hours} \]

### Step 5: Determine the meeting time.
- The second train starts at 9 a.m. and they meet after 2 hours.
- Therefore, the time they meet is:
\[ 9 \, \text{a.m.} + 2 \, \text{hours} = 11 \, \text{a.m.} \]

### Final Answer:
The two trains meet at **11 a.m.**.

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