K walked at 3 kmph for a certain distance with L and thereafter at 6 kmph with M to cover a total distance of 27 km in 7 hours. Find the distance travelled with M.
A. 15 km
B. 12 km
C. 10 km
D. 9 km

Options

A. B
B. A
C. C
D. D

Answer

To solve the problem, we need to determine the distance K traveled with M. We will break down the solution step by step.

### Step 1: Define Variables
Let:
- \( X \) = time (in hours) K walked with L
- \( Y \) = time (in hours) K walked with M

### Step 2: Set Up the Equations
From the problem, we know:
1. The total time K walked is 7 hours:
\[ X + Y = 7 \quad \text{(Equation 1)} \]

2. The total distance K covered is 27 km. The distance traveled with L at 3 km/h is \( 3X \) and the distance traveled with M at 6 km/h is \( 6Y \):
\[ 3X + 6Y = 27 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
We can simplify Equation 2 by dividing everything by 3:
\[ X + 2Y = 9 \quad \text{(Equation 3)} \]

### Step 4: Solve the System of Equations
Now we have two equations:
1. \( X + Y = 7 \) (Equation 1)
2. \( X + 2Y = 9 \) (Equation 3)

We can subtract Equation 1 from Equation 3:
\[ (X + 2Y) - (X + Y) = 9 - 7 \]
This simplifies to:
\[ Y = 2 \]

### Step 5: Find X
Now substitute \( Y = 2 \) back into Equation 1 to find \( X \):
\[ X + 2 = 7 \]
\[ X = 5 \]

### Step 6: Calculate the Distance with M
Now that we have \( Y \), we can find the distance traveled with M:
\[ \text{Distance with M} = 6Y = 6 \times 2 = 12 \text{ km} \]

### Conclusion
The distance traveled by K with M is **12 km**.