A person can stream a boat of 5 km/h in still water. If he takes 1 hour to go and return from place and speed of current is 1 km/h. What will be the distance.
एक व्यक्ति शान्त जल में 5 किमी/घं. की चाल से नाव चला सकता है। यदि किसी स्थान पर नाव द्वारा जाने तथा वापस आने में उसे एक घण्टे का समय लगता है जबकि धारा की गति 1 किमी./घ० है, तो स्थान कितनी दूर होगी?

Options

A. 2.5 किमी.
B. 3 किमी.
C. 2.4 किमी.
D. 3.6 किमी.

Explanation

To solve the problem, we need to determine the distance to the place based on the given speeds and time taken for the round trip. Let's break it down step by step.

### Step 1: Understand the speeds
- The speed of the boat in still water is 5 km/h.
- The speed of the current is 1 km/h.

### Step 2: Calculate downstream and upstream speeds
- **Downstream speed (DSS)**: This is the speed of the boat plus the speed of the current.
\[ \text{DSS} = \text{Speed of boat} + \text{Speed of current} = 5 \text{ km/h} + 1 \text{ km/h} = 6 \text{ km/h} \]

- **Upstream speed (USS)**: This is the speed of the boat minus the speed of the current.
\[ \text{USS} = \text{Speed of boat} - \text{Speed of current} = 5 \text{ km/h} - 1 \text{ km/h} = 4 \text{ km/h} \]

### Step 3: Set up the equation for distance
Let the distance to the place be \( d \) km. The time taken to go downstream and upstream can be expressed as:
- Time taken downstream = \( \frac{d}{\text{DSS}} = \frac{d}{6} \)
- Time taken upstream = \( \frac{d}{\text{USS}} = \frac{d}{4} \)

### Step 4: Total time for the round trip
The total time for the round trip is given as 1 hour. Therefore, we can write the equation:
\[ \frac{d}{6} + \frac{d}{4} = 1 \]

### Step 5: Solve the equation
To solve this equation, we need a common denominator. The least common multiple of 6 and 4 is 12. Rewriting the equation:
\[ \frac{2d}{12} + \frac{3d}{12} = 1 \]
Combining the fractions:
\[ \frac{5d}{12} = 1 \]
Now, multiply both sides by 12 to eliminate the denominator:
\[ 5d = 12 \]
Now, divide both sides by 5:
\[ d = \frac{12}{5} = 2.4 \text{ km} \]

### Final Answer
The distance to the place is **2.4 km**.

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