Two people A and B are at a distance of 260 km from each other at 9 : 00 a.m. A immediately starts moving towards B at a speed of 25 km/h and at 11 : 00 a.m. b starts moving towards A at a speed of 10 km/hr. At what time (in p.m) will they meet each other ?

Options

A. `5 : 00`
B. `6 : 00`
C. `6 : 30`
D. `7 : 00`

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine the distance covered by A before B starts moving
- A starts moving at 9:00 a.m. at a speed of 25 km/h.
- B starts moving at 11:00 a.m.
- The time from 9:00 a.m. to 11:00 a.m. is 2 hours.

**Distance covered by A in 2 hours:**
\[ \text{Distance} = \text{Speed} \times \text{Time} = 25 \, \text{km/h} \times 2 \, \text{h} = 50 \, \text{km} \]

### Step 2: Calculate the remaining distance between A and B after 2 hours
- Initial distance between A and B = 260 km
- Distance covered by A = 50 km

**Remaining distance:**
\[ \text{Remaining Distance} = 260 \, \text{km} - 50 \, \text{km} = 210 \, \text{km} \]

### Step 3: Calculate the relative speed of A and B after B starts moving
- Speed of A = 25 km/h
- Speed of B = 10 km/h

**Relative speed:**
\[ \text{Relative Speed} = \text{Speed of A} + \text{Speed of B} = 25 \, \text{km/h} + 10 \, \text{km/h} = 35 \, \text{km/h} \]

### Step 4: Calculate the time taken for A and B to meet after B starts moving
- Remaining distance = 210 km
- Relative speed = 35 km/h

**Time to meet:**
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{210 \, \text{km}}{35 \, \text{km/h}} = 6 \, \text{hours} \]

### Step 5: Determine the meeting time
- B starts moving at 11:00 a.m.
- They will meet after 6 hours from 11:00 a.m.

**Meeting time:**
\[ 11:00 \, \text{a.m.} + 6 \, \text{hours} = 5:00 \, \text{p.m.} \]

### Final Answer
A and B will meet at **5:00 p.m.**