The distance of two cities A and B is 22 km. A cyclist startss to go from A to B at a speed of 8 km/h and after half an hour another cyclist start to go from B to A at a speed of 10 kmph. How far from A will they meet ?

Options

A. 6 km
B. 10 km
C. 11 km
D. 12 km

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the time taken by the first cyclist before the second cyclist starts.
The first cyclist starts from city A to city B at a speed of 8 km/h. The second cyclist starts half an hour later from city B to city A at a speed of 10 km/h.

**Calculation:**
- Time taken by the first cyclist before the second cyclist starts = 0.5 hours

### Step 2: Calculate the distance covered by the first cyclist in that time.
Using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

**Calculation:**
- Distance covered by the first cyclist = 8 km/h × 0.5 h = 4 km

### Step 3: Determine the remaining distance between the two cyclists when the second cyclist starts.
The total distance between A and B is 22 km. After the first cyclist has traveled 4 km, the remaining distance is:

**Calculation:**
- Remaining distance = 22 km - 4 km = 18 km

### Step 4: Calculate the relative speed of both cyclists.
When the second cyclist starts, both cyclists are moving towards each other. Therefore, we can add their speeds to find the relative speed.

**Calculation:**
- Speed of the first cyclist = 8 km/h
- Speed of the second cyclist = 10 km/h
- Relative speed = 8 km/h + 10 km/h = 18 km/h

### Step 5: Calculate the time taken to meet after the second cyclist starts.
Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

**Calculation:**
- Time taken to meet = Remaining distance / Relative speed = 18 km / 18 km/h = 1 hour

### Step 6: Calculate the distance traveled by the first cyclist during this time.
Now, we can find out how far the first cyclist travels in this time.

**Calculation:**
- Distance traveled by the first cyclist in 1 hour = Speed × Time = 8 km/h × 1 h = 8 km

### Step 7: Calculate the total distance from A to the meeting point.
The total distance from A to the meeting point is the distance covered by the first cyclist before the second cyclist started plus the distance traveled by the first cyclist after the second cyclist started.

**Calculation:**
- Total distance from A = Distance before second cyclist started + Distance after = 4 km + 8 km = 12 km

### Final Answer:
The two cyclists will meet 12 km from city A.

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