A boat takes a total time of 5 hours to cover a distance of 60 km upstream and 60 km downstream. If the speed of the boat in still water is `400%` more than the speed of the river current, what is the speed of the boat in still water? (in kmph)

Options

A. 25
B. 30
C. 20
D. 18

Answer

To solve the problem, we need to determine the speed of the boat in still water given that it takes a total of 5 hours to cover 60 km upstream and 60 km downstream, and that the speed of the boat in still water is 400% more than the speed of the river current.

### Step-by-Step Solution:

1. **Define Variables:**
Let the speed of the river current be \( x \) km/h.
Therefore, the speed of the boat in still water will be \( 5x \) km/h (since 400% more than \( x \) means \( x + 4x = 5x \)).

2. **Calculate Effective Speeds:**
- The effective speed of the boat when going upstream (against the current) is:
\[ \text{Speed upstream} = \text{Speed of boat} - \text{Speed of current} = 5x - x = 4x \text{ km/h} \]
- The effective speed of the boat when going downstream (with the current) is:
\[ \text{Speed downstream} = \text{Speed of boat} + \text{Speed of current} = 5x + x = 6x \text{ km/h} \]

3. **Calculate Time Taken for Each Journey:**
- Time taken to travel upstream:
\[ \text{Time upstream} = \frac{\text{Distance}}{\text{Speed}} = \frac{60}{4x} = \frac{15}{x} \text{ hours} \]
- Time taken to travel downstream:
\[ \text{Time downstream} = \frac{\text{Distance}}{\text{Speed}} = \frac{60}{6x} = \frac{10}{x} \text{ hours} \]

4. **Set Up the Total Time Equation:**
The total time taken for both upstream and downstream is given as 5 hours:
\[ \text{Time upstream} + \text{Time downstream} = 5 \]
Substituting the expressions for time:
\[ \frac{15}{x} + \frac{10}{x} = 5 \]

5. **Combine and Solve for \( x \):**
Combine the fractions:
\[ \frac{15 + 10}{x} = 5 \implies \frac{25}{x} = 5 \]
Cross-multiplying gives:
\[ 25 = 5x \implies x = 5 \text{ km/h} \]

6. **Calculate the Speed of the Boat in Still Water:**
Now that we have \( x \), we can find the speed of the boat in still water:
\[ \text{Speed of boat in still water} = 5x = 5 \times 5 = 25 \text{ km/h} \]

### Final Answer:
The speed of the boat in still water is **25 km/h**.