A train leaves meerut at 6a.m.and reaches delhi at 10a.m. another train leaves delhi at 8 a.m. and reaches meerut at 11.30 .m.at what time do the trains cross one another

Options

A. 9.26a.m.
B. 9a.m.
C. 8.36a.m.
D. 8.56a.m.

Answer

To solve the problem of when the two trains cross each other, we can follow these steps:

### Step 1: Determine the time taken by each train
- The first train leaves Meerut at 6 a.m. and reaches Delhi at 10 a.m.
- Time taken = 10 a.m. - 6 a.m. = 4 hours.

- The second train leaves Delhi at 8 a.m. and reaches Meerut at 11:30 a.m.
- Time taken = 11:30 a.m. - 8 a.m. = 3.5 hours.

### Step 2: Calculate the speeds of the trains
Let the distance between Meerut and Delhi be \( y \) km.

- Speed of the first train (from Meerut to Delhi):
\[ \text{Speed}_1 = \frac{y}{4} \text{ km/h} \]

- Speed of the second train (from Delhi to Meerut):
\[ \text{Speed}_2 = \frac{y}{3.5} \text{ km/h} = \frac{2y}{7} \text{ km/h} \]

### Step 3: Set up the equation for the distance covered until they meet
Let \( t \) be the time in hours after 6 a.m. when the trains cross each other.

- Distance covered by the first train in \( t \) hours:
\[ \text{Distance}_1 = \text{Speed}_1 \times t = \frac{y}{4} \times t \]

- Distance covered by the second train after it starts at 8 a.m. (which is \( t - 2 \) hours since it starts 2 hours later):
\[ \text{Distance}_2 = \text{Speed}_2 \times (t - 2) = \frac{2y}{7} \times (t - 2) \]

### Step 4: Set the total distance equal to \( y \)
Since both trains together cover the distance \( y \) km when they meet:
\[ \frac{y}{4} \times t + \frac{2y}{7} \times (t - 2) = y \]

### Step 5: Simplify the equation
Dividing through by \( y \) (assuming \( y \neq 0 \)):
\[ \frac{t}{4} + \frac{2}{7}(t - 2) = 1 \]

### Step 6: Clear the fractions
Multiply through by 28 (the least common multiple of 4 and 7):
\[ 7t + 8(t - 2) = 28 \]
\[ 7t + 8t - 16 = 28 \]
\[ 15t - 16 = 28 \]
\[ 15t = 44 \]
\[ t = \frac{44}{15} \approx 2.93 \text{ hours} \]

### Step 7: Convert time into hours and minutes
- \( 2.93 \) hours is approximately \( 2 \) hours and \( 56 \) minutes.
- Therefore, the trains cross each other at:
\[ 6:00 \text{ a.m.} + 2 \text{ hours and } 56 \text{ minutes} = 8:56 \text{ a.m.} \]

### Conclusion
The two trains cross each other at **8:56 a.m.**

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