The distance between Bandel and Asansol is 100 km. A leaves Bandel for Asansol and walks at the rate of 3 km/hr. 3 hrs later, B starts from Asansol for Bandel and walks at 3.5 km/hr. Find the distance from Asansol where they would meet?

Options

A. 51 km
B. 49 km
C. 53 km
D. 52 km

Answer

To solve the problem step by step, let's break it down clearly:

### Step 1: Understand the scenario
A leaves Bandel for Asansol and walks at a speed of 3 km/hr. B starts 3 hours later from Asansol towards Bandel at a speed of 3.5 km/hr. The total distance between Bandel and Asansol is 100 km.

### Step 2: Define the variables
- Let \( t \) be the total time in hours that A has been walking when they meet.
- Since B starts 3 hours later, the time B has been walking is \( t - 3 \).

### Step 3: Calculate the distance traveled by A
The distance traveled by A when they meet can be expressed as:
\[ D_A = \text{Speed of A} \times \text{Time of A} = 3 \text{ km/hr} \times t = 3t \]

### Step 4: Calculate the distance traveled by B
The distance traveled by B when they meet can be expressed as:
\[ D_B = \text{Speed of B} \times \text{Time of B} = 3.5 \text{ km/hr} \times (t - 3) = 3.5(t - 3) \]

### Step 5: Set up the equation
Since the total distance between Bandel and Asansol is 100 km, we can write:
\[ D_A + D_B = 100 \]
Substituting the distances we found:
\[ 3t + 3.5(t - 3) = 100 \]

### Step 6: Simplify the equation
Expanding the equation:
\[ 3t + 3.5t - 10.5 = 100 \]
Combine like terms:
\[ 6.5t - 10.5 = 100 \]

### Step 7: Solve for \( t \)
Add 10.5 to both sides:
\[ 6.5t = 110.5 \]
Now, divide both sides by 6.5:
\[ t = \frac{110.5}{6.5} \]
Calculating this gives:
\[ t = 17 \text{ hours} \]

### Step 8: Calculate the distance traveled by A
Now, substituting \( t \) back into the equation for \( D_A \):
\[ D_A = 3t = 3 \times 17 = 51 \text{ km} \]

### Step 9: Calculate the distance from Asansol where they meet
To find the distance from Asansol where they meet, we subtract the distance traveled by A from the total distance:
\[ D_B = 100 - D_A = 100 - 51 = 49 \text{ km} \]

### Final Answer
The distance from Asansol where A and B meet is **49 km**.

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