A man covers one-fifth of his journey on foot, two-thirds by car, and the remaining 4 km by taxi. Find the total distance covered by the man.

Options

A. `24` km
B. `50` km
C. `10` km
D. `30` km

Answer

To solve the problem, we will follow these steps:

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

### Step 2: Calculate the distance covered on foot
The distance covered on foot is given as one-fifth of the total distance:
\[ \text{Distance on foot} = \frac{1}{5}x \]

### Step 3: Calculate the distance covered by car
The distance covered by car is given as two-thirds of the total distance:
\[ \text{Distance by car} = \frac{2}{3}x \]

### Step 4: Calculate the remaining distance covered by taxi
It is given that the remaining distance covered by taxi is 4 km. Therefore, we can express this as:
\[ \text{Remaining distance} = x - \left(\frac{1}{5}x + \frac{2}{3}x\right) = 4 \]

### Step 5: Combine the distances and set up the equation
Now, we will combine the distances covered on foot and by car:
\[ \frac{1}{5}x + \frac{2}{3}x \]
To combine these fractions, we need a common denominator. The least common multiple of 5 and 3 is 15. Thus, we rewrite the fractions:
\[ \frac{1}{5}x = \frac{3}{15}x \quad \text{and} \quad \frac{2}{3}x = \frac{10}{15}x \]
Now we can add them:
\[ \frac{3}{15}x + \frac{10}{15}x = \frac{13}{15}x \]

### Step 6: Substitute back into the equation
Now we substitute this back into our equation:
\[ x - \frac{13}{15}x = 4 \]

### Step 7: Simplify the equation
This simplifies to:
\[ \frac{2}{15}x = 4 \]

### Step 8: Solve for \( x \)
To find \( x \), we multiply both sides by \( \frac{15}{2} \):
\[ x = 4 \times \frac{15}{2} = 30 \]

### Conclusion
The total distance covered by the man is \( \boxed{30} \) kilometers.

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