A man starts walking from a place X and reaches the place Y in 12 hours. He travels 3/7th of the total distance at the speed of 3 km/hr and the remaining distance at the speed of 4 km/hr. What is the distance (in km) between X and Y?

Options

A. 28
B. 36
C. 40
D. 42

Answer

To solve the problem step by step, we will follow the information given in the question and apply the relevant formulas.

### Step 1: Define the total distance
Let the total distance between places X and Y be \( D \). According to the question, the man travels \( \frac{3}{7} \) of the total distance at a speed of 3 km/hr.

### Step 2: Calculate the distance for the first part
The distance covered in the first part is:
\[ D_1 = \frac{3}{7}D \]

### Step 3: Calculate the remaining distance
The remaining distance is:
\[ D_2 = D - D_1 = D - \frac{3}{7}D = \frac{4}{7}D \]

### Step 4: Calculate the time taken for each part
Using the formula for time, \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \):

1. Time taken for the first part:
\[ T_1 = \frac{D_1}{3} = \frac{\frac{3}{7}D}{3} = \frac{1}{7}D \]

2. Time taken for the second part:
\[ T_2 = \frac{D_2}{4} = \frac{\frac{4}{7}D}{4} = \frac{1}{7}D \]

### Step 5: Total time taken
The total time taken for the journey is given as 12 hours:
\[ T_1 + T_2 = 12 \]
Substituting the expressions for \( T_1 \) and \( T_2 \):
\[ \frac{1}{7}D + \frac{1}{7}D = 12 \]
\[ \frac{2}{7}D = 12 \]

### Step 6: Solve for \( D \)
To find \( D \), multiply both sides by 7:
\[ 2D = 12 \times 7 \]
\[ 2D = 84 \]
Now divide by 2:
\[ D = 42 \text{ km} \]

### Final Answer
The distance between X and Y is **42 km**.

---