एक व्यक्ति अपनी यात्रा का 2/5 ट्रेन से, एक तिहाई बस से, एक चौथाई कार से तथा 3km पैदल तय करता है। व्यक्ति द्वारा तय की गई दूरी बतायें -

Options

A. 180
B. 160
C. 160
D. 140

Answer

**Step-by-Step Solution:**

1. **Assume the Total Distance**:
Let's assume the total distance of the journey is \( x \) kilometers.

2. **Distance by Train**:
The person travels \( \frac{2}{5} \) of the total distance by train.
Therefore, the distance by train is:
\[ \text{Distance by Train} = \frac{2}{5}x \]

3. **Distance by Bus**:
The person travels \( \frac{1}{3} \) of the total distance by bus.
Therefore, the distance by bus is:
\[ \text{Distance by Bus} = \frac{1}{3}x \]

4. **Distance by Car**:
The person travels \( \frac{1}{4} \) of the total distance by car.
Therefore, the distance by car is:
\[ \text{Distance by Car} = \frac{1}{4}x \]

5. **Distance on Foot**:
The person also travels 3 km on foot.
Therefore, the distance on foot is:
\[ \text{Distance on Foot} = 3 \text{ km} \]

6. **Setting Up the Equation**:
The sum of all these distances should equal the total distance \( x \):
\[ \frac{2}{5}x + \frac{1}{3}x + \frac{1}{4}x + 3 = x \]

7. **Finding a Common Denominator**:
To solve the equation, we need a common denominator for the fractions. The least common multiple (LCM) of 5, 3, and 4 is 60.

8. **Rewriting the Fractions**:
Convert each fraction to have a denominator of 60:
\[ \frac{2}{5}x = \frac{24}{60}x, \quad \frac{1}{3}x = \frac{20}{60}x, \quad \frac{1}{4}x = \frac{15}{60}x \]

9. **Substituting Back into the Equation**:
Substitute these back into the equation:
\[ \frac{24}{60}x + \frac{20}{60}x + \frac{15}{60}x + 3 = x \]

10. **Combining the Terms**:
Combine the fractions on the left side:
\[ \frac{24 + 20 + 15}{60}x + 3 = x \]
\[ \frac{59}{60}x + 3 = x \]

11. **Isolating \( x \)**:
Subtract \( \frac{59}{60}x \) from both sides:
\[ 3 = x - \frac{59}{60}x \]
\[ 3 = \frac{1}{60}x \]

12. **Solving for \( x \)**:
Multiply both sides by 60 to solve for \( x \):
\[ x = 3 \times 60 = 180 \text{ km} \]

**Final Answer**:
The total distance traveled by the person is **180 kilometers**.

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