A man starts running from point P at 11:00 a.m. with a speed of 10 km/hr. He runs for 2 hourse and then takes a 1 hour rest. He continues this till he is caught by another man who starts at 2:00 pm from point P and runs non- stop at a speed of 15 km/hr towards the first man. At what time (in pm) will the first man be caught?

Options

A. `6:20`
B. `4: 40`
C. `6:00`
D. `5:30`

Answer

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

### Step 1: Determine the distance covered by the first man before the second man starts running.

- The first man starts running at 11:00 a.m. and runs for 2 hours at a speed of 10 km/hr.
- Distance covered in 2 hours = Speed × Time = 10 km/hr × 2 hr = 20 km.

### Step 2: Calculate the time until the second man starts running.

- The second man starts running at 2:00 p.m.
- The first man runs from 11:00 a.m. to 2:00 p.m., which is a total of 3 hours.
- In these 3 hours, he runs for 2 hours and takes a 1-hour rest.
- Therefore, he runs for 2 hours and rests for 1 hour, which means he has covered 20 km by 2:00 p.m.

### Step 3: Determine the distance between the two men when the second man starts running.

- At 2:00 p.m., the first man has covered 20 km, so he is 20 km away from point P.

### Step 4: Calculate the speeds of both men.

- Speed of the first man = 10 km/hr.
- Speed of the second man = 15 km/hr.

### Step 5: Calculate the relative speed of the second man with respect to the first man.

- The second man is running towards the first man, so their relative speed = Speed of second man - Speed of first man = 15 km/hr - 10 km/hr = 5 km/hr.

### Step 6: Calculate the time taken for the second man to catch the first man.

- Distance to be covered by the second man = 20 km (the distance between them when the second man starts).
- Time taken to catch the first man = Distance / Relative Speed = 20 km / 5 km/hr = 4 hours.

### Step 7: Determine the time at which the first man is caught.

- The second man starts running at 2:00 p.m. and takes 4 hours to catch the first man.
- Therefore, the time when the first man is caught = 2:00 p.m. + 4 hours = 6:00 p.m.

### Final Answer:
The first man will be caught at **6:00 p.m.**.

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