A boat goes 75 km upstream in 3 hours and 60 km downstream in 1.5 hours .The speed of the boat in still water is :

Options

A. 32 . 5 kmph
B. 30 kmph
C. 65 kmph
D. 60 kmph

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the speed upstream
Given:
- Distance upstream = 75 km
- Time taken upstream = 3 hours

Using the formula for speed:
\[ \text{Speed upstream} = \frac{\text{Distance upstream}}{\text{Time taken upstream}} = \frac{75 \text{ km}}{3 \text{ hours}} = 25 \text{ km/h} \]

### Step 2: Calculate the speed downstream
Given:
- Distance downstream = 60 km
- Time taken downstream = 1.5 hours

Using the formula for speed:
\[ \text{Speed downstream} = \frac{\text{Distance downstream}}{\text{Time taken downstream}} = \frac{60 \text{ km}}{1.5 \text{ hours}} = 40 \text{ km/h} \]

### Step 3: Calculate the speed of the boat in still water
The speed of the boat in still water can be calculated using the formula:
\[ \text{Speed of boat in still water} = \frac{\text{Speed upstream} + \text{Speed downstream}}{2} \]

Substituting the values we found:
\[ \text{Speed of boat in still water} = \frac{25 \text{ km/h} + 40 \text{ km/h}}{2} = \frac{65 \text{ km/h}}{2} = 32.5 \text{ km/h} \]

### Conclusion
The speed of the boat in still water is **32.5 km/h**.

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