A person covers a distance by a train running at 25 km/h and he covers same distance while returning on foot at the speed of 4 km/h. If he took 5 hours 48 minutes in his whole journey then distance was -
किसी व्यक्ति ने 25किमी./घं की चाल से चलने वाली रेलगाड़ी द्वारा एक दूरी तय की तथा वही दूरी वापसी में उसने 4 किमी/घं की चाल से पैदल चलकर तय की। यदि आने-जाने में उसे कुल समय 5 घण्टे 48 मिनट लगा हो, तो दूरी थी -

Options

A. 25 किमी.
B. 30 किमी.
C. 20 किमी.
D. 15 किमी.

Explanation

To solve the problem step by step, we can follow these instructions:

### Step 1: Convert the total time into hours
The total time taken for the journey is given as 5 hours 48 minutes. We need to convert this into hours.

\[ 5 \text{ hours} + \frac{48 \text{ minutes}}{60} = 5 + 0.8 = 5.8 \text{ hours} \]

### Step 2: Let the distance be \( x \) km
Assume the distance covered by the train and on foot is \( x \) km.

### Step 3: Calculate the time taken for each part of the journey
- Time taken by the train to cover \( x \) km at 25 km/h:
\[ \text{Time}_{\text{train}} = \frac{x}{25} \]

- Time taken on foot to cover \( x \) km at 4 km/h:
\[ \text{Time}_{\text{foot}} = \frac{x}{4} \]

### Step 4: Set up the equation for total time
The total time for the journey is the sum of the time taken by the train and the time taken on foot, which equals 5.8 hours:
\[ \frac{x}{25} + \frac{x}{4} = 5.8 \]

### Step 5: Find a common denominator and solve for \( x \)
The common denominator for 25 and 4 is 100. Rewrite the equation:
\[ \frac{4x}{100} + \frac{25x}{100} = 5.8 \]

Combine the fractions:
\[ \frac{4x + 25x}{100} = 5.8 \]
\[ \frac{29x}{100} = 5.8 \]

### Step 6: Multiply both sides by 100 to eliminate the fraction
\[ 29x = 580 \]

### Step 7: Solve for \( x \)
\[ x = \frac{580}{29} = 20 \text{ km} \]

### Final Answer
The distance was **20 km**.

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