Distance between A and B is 72km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed 4 km/h.While the other man travelled with varying speed as follows In first hour,his speed was 2 km/h,in the second hour,it was 2.5km/h,in the third hour,it was 3km/h, and soon. When will they meet each other?

Options

A. 7H
B. 10h
C. 35 km from A
D. midway betweeen A and 8

Answer

To solve the problem step by step, we need to determine when the two men meet as they walk towards each other from points A and B.

### Step 1: Understand the speeds and distances
- The distance between A and B is 72 km.
- The man starting from A travels at a constant speed of 4 km/h.
- The man starting from B has varying speeds:
- 1st hour: 2 km/h
- 2nd hour: 2.5 km/h
- 3rd hour: 3 km/h
- 4th hour: 3.5 km/h
- 5th hour: 4 km/h
- 6th hour: 4.5 km/h
- and so on, increasing by 0.5 km/h each hour.

### Step 2: Calculate the distance covered each hour
- **1st hour**:
- Distance by A = 4 km
- Distance by B = 2 km
- Total distance = 4 + 2 = 6 km

- **2nd hour**:
- Distance by A = 4 km
- Distance by B = 2.5 km
- Total distance = 4 + 2.5 = 6.5 km

- **3rd hour**:
- Distance by A = 4 km
- Distance by B = 3 km
- Total distance = 4 + 3 = 7 km

- **4th hour**:
- Distance by A = 4 km
- Distance by B = 3.5 km
- Total distance = 4 + 3.5 = 7.5 km

- **5th hour**:
- Distance by A = 4 km
- Distance by B = 4 km
- Total distance = 4 + 4 = 8 km

- **6th hour**:
- Distance by A = 4 km
- Distance by B = 4.5 km
- Total distance = 4 + 4.5 = 8.5 km

- **7th hour**:
- Distance by A = 4 km
- Distance by B = 5 km
- Total distance = 4 + 5 = 9 km

- **8th hour**:
- Distance by A = 4 km
- Distance by B = 5.5 km
- Total distance = 4 + 5.5 = 9.5 km

- **9th hour**:
- Distance by A = 4 km
- Distance by B = 6 km
- Total distance = 4 + 6 = 10 km

### Step 3: Calculate cumulative distance
Now, we will add the distances covered each hour until we reach or exceed 72 km.

- After 1st hour: 6 km
- After 2nd hour: 6 + 6.5 = 12.5 km
- After 3rd hour: 12.5 + 7 = 19.5 km
- After 4th hour: 19.5 + 7.5 = 27 km
- After 5th hour: 27 + 8 = 35 km
- After 6th hour: 35 + 8.5 = 43.5 km
- After 7th hour: 43.5 + 9 = 52.5 km
- After 8th hour: 52.5 + 9.5 = 62 km
- After 9th hour: 62 + 10 = 72 km

### Step 4: Determine the meeting point
They meet after 9 hours. To find the distance traveled by the man from A:
- Distance = Speed × Time = 4 km/h × 9 hours = 36 km.

Thus, they meet at the point which is 36 km from A and 36 km from B.

### Final Answer
They will meet after 9 hours at a distance of 36 km from point A.