the speed of a boat along the stream is 12 km /h and againts the stream is 8 km /h .The time taken by the boat to sail 24 km in still water is

Options

A. 2 hours
B. 3 hours
C. 2.4 hours
D. 1.2 hours

Answer

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

### Step 1: Understand the Given Information
We are given:
- Speed of the boat downstream (with the stream) = 12 km/h
- Speed of the boat upstream (against the stream) = 8 km/h

### Step 2: Calculate the Speed of the Boat in Still Water
The speed of the boat in still water can be calculated using the formula:
\[ \text{Speed in still water} = \frac{\text{Speed downstream} + \text{Speed upstream}}{2} \]
Substituting the values:
\[ \text{Speed in still water} = \frac{12 \text{ km/h} + 8 \text{ km/h}}{2} = \frac{20 \text{ km/h}}{2} = 10 \text{ km/h} \]

### Step 3: Calculate the Time Taken to Sail 24 km in Still Water
We know the formula for time is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Here, the distance is 24 km and the speed in still water is 10 km/h. Thus:
\[ \text{Time} = \frac{24 \text{ km}}{10 \text{ km/h}} = 2.4 \text{ hours} \]

### Final Answer
The time taken by the boat to sail 24 km in still water is **2.4 hours**.

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