Anil travels from place `A` to place `B` and Akhil travels form place `A`. Anil travels one- third of the distance and Akhil travels one-fourth of the distance. The distance travelled by Anil is o`1km` more than the distance travelled by Akhil. What is the distance between place `A` and place `B` ? (In `km`)

Options

A. `9`
B. `10`
C. `12`
D. `18`

Answer

To solve the problem step by step, we will define the total distance between place A and place B as \( D \) kilometers.

### Step 1: Define the distances traveled by Anil and Akhil
- Anil travels one-third of the distance:
\[ \text{Distance traveled by Anil} = \frac{D}{3} \]
- Akhil travels one-fourth of the distance:
\[ \text{Distance traveled by Akhil} = \frac{D}{4} \]

### Step 2: Set up the equation based on the information given
According to the problem, the distance traveled by Anil is 1 km more than the distance traveled by Akhil. Therefore, we can write the equation:
\[ \frac{D}{3} = \frac{D}{4} + 1 \]

### Step 3: Eliminate the fractions
To eliminate the fractions, we can find a common denominator. The least common multiple (LCM) of 3 and 4 is 12. We will multiply every term in the equation by 12:
\[ 12 \cdot \frac{D}{3} = 12 \cdot \left(\frac{D}{4} + 1\right) \]
This simplifies to:
\[ 4D = 3D + 12 \]

### Step 4: Solve for \( D \)
Now, we will isolate \( D \) by subtracting \( 3D \) from both sides:
\[ 4D - 3D = 12 \]
This simplifies to:
\[ D = 12 \]

### Conclusion
The total distance between place A and place B is:
\[ \text{Distance} = 12 \text{ km} \]