Distance of point P and Q is 500 metre. Two person A and B moving from P and Q on same time in same distance those speed are 15 km/hr and 13 km/hr respectively. How much distance will left b/w left after 3 minutes ?

Options

A. 300 m
B. 400 m
C. 200 m
D. 100 m

Answer

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

### Step 1: Convert Speeds from km/hr to m/s
We know that:
- Speed of A = 15 km/hr
- Speed of B = 13 km/hr

To convert km/hr to m/s, we use the conversion factor \( \frac{5}{18} \).

\[ \text{Speed of A in m/s} = 15 \times \frac{5}{18} = \frac{75}{18} = 4.17 \text{ m/s} \]
\[ \text{Speed of B in m/s} = 13 \times \frac{5}{18} = \frac{65}{18} = 3.61 \text{ m/s} \]

### Step 2: Calculate the Relative Speed
Since A and B are moving towards each other, we can find their relative speed by adding their speeds.

\[ \text{Relative Speed} = \text{Speed of A} + \text{Speed of B} = 4.17 + 3.61 = 7.78 \text{ m/s} \]

### Step 3: Calculate the Distance Covered in 3 Minutes
First, we convert 3 minutes into seconds:
\[ 3 \text{ minutes} = 3 \times 60 = 180 \text{ seconds} \]

Now, we can calculate the distance covered in 3 minutes using the relative speed:
\[ \text{Distance covered} = \text{Relative Speed} \times \text{Time} = 7.78 \times 180 = 1400.4 \text{ meters} \]

### Step 4: Calculate the Remaining Distance
Initially, the distance between points P and Q is 500 meters. After 3 minutes, we need to find the remaining distance between A and B.

Since they are moving towards each other, we need to subtract the distance they have covered from the initial distance:
\[ \text{Remaining Distance} = \text{Initial Distance} - \text{Distance Covered} \]
However, we realize that the distance covered (1400.4 meters) is greater than the initial distance (500 meters), which means they have crossed each other.

Thus, the remaining distance is:
\[ \text{Remaining Distance} = 0 \text{ meters} \]

### Final Answer
After 3 minutes, the distance left between A and B is 0 meters.

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