A man while returning from his factory, travels `2/3` of the distance by bus and `3/4` of the rest by car, and the remaining by foot. If he travels 2 km on foot, find the distance covered by him.

Options

A. 24 km
B. 22 km
C. 28 km
D. 26 km

Answer

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

### Step 1: Define the total distance
Let the total distance covered by the man be \( D \) kilometers.

### Step 2: Calculate the distance traveled by bus
The man travels \( \frac{2}{3} \) of the total distance by bus. Therefore, the distance traveled by bus is:
\[ \text{Distance by bus} = \frac{2}{3}D \]

### Step 3: Calculate the remaining distance after the bus
After traveling by bus, the remaining distance is:
\[ \text{Remaining distance} = D - \frac{2}{3}D = \frac{1}{3}D \]

### Step 4: Calculate the distance traveled by car
The man then travels \( \frac{3}{4} \) of the remaining distance by car. The distance traveled by car is:
\[ \text{Distance by car} = \frac{3}{4} \times \frac{1}{3}D = \frac{3}{12}D = \frac{1}{4}D \]

### Step 5: Calculate the remaining distance after the car
After traveling by car, the remaining distance is:
\[ \text{Remaining distance} = \frac{1}{3}D - \frac{1}{4}D \]
To subtract these fractions, we need a common denominator. The least common multiple of 3 and 4 is 12. Therefore:
\[ \frac{1}{3}D = \frac{4}{12}D \quad \text{and} \quad \frac{1}{4}D = \frac{3}{12}D \]
Now, we can subtract:
\[ \text{Remaining distance} = \frac{4}{12}D - \frac{3}{12}D = \frac{1}{12}D \]

### Step 6: Set up the equation with the distance traveled on foot
According to the problem, the distance traveled on foot is 2 km. Therefore, we can set up the equation:
\[ \frac{1}{12}D = 2 \]

### Step 7: Solve for \( D \)
To find \( D \), multiply both sides of the equation by 12:
\[ D = 2 \times 12 = 24 \text{ km} \]

### Conclusion
The total distance covered by the man is \( 24 \) kilometers.

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