Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer
What is the speed of a boat in still water ?
I The boat covers a distance of 160 km in 8 hours Whilerúnning upstream.
II It covers the same distance in 4 hours while running downstream

Options

A. A)if the data in statement I alone
are sufficient to answer the question,
while the data in statement II alone
are not sufficient
to answer the question.
B. B)if the data in statement II
alone are sufficient to answer the question,
while the data in statement I alone
are not sufficient to answer the question.
C. C)If the data either in statement
I alone or in statement II alone
are sufficient to answer the question.
D. D)if the data in both statement
I and II together are necessary
to answer the question.

Answer

To determine the speed of a boat in still water, we will analyze the information provided in the two statements step by step.

### Step 1: Analyze Statement I
**Statement I:** The boat covers a distance of 160 km in 8 hours while running upstream.

- To find the upstream speed, we use the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- Substituting the values:
\[ \text{Upstream Speed} = \frac{160 \text{ km}}{8 \text{ hours}} = 20 \text{ km/h} \]
- The upstream speed can be expressed as:
\[ \text{Upstream Speed} = \text{Speed of the boat} - \text{Speed of the water} \]
- Therefore, we have:
\[ \text{Speed of the boat} - \text{Speed of the water} = 20 \quad \text{(Equation 1)} \]

### Step 2: Analyze Statement II
**Statement II:** The boat covers the same distance in 4 hours while running downstream.

- To find the downstream speed, we again use the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- Substituting the values:
\[ \text{Downstream Speed} = \frac{160 \text{ km}}{4 \text{ hours}} = 40 \text{ km/h} \]
- The downstream speed can be expressed as:
\[ \text{Downstream Speed} = \text{Speed of the boat} + \text{Speed of the water} \]
- Therefore, we have:
\[ \text{Speed of the boat} + \text{Speed of the water} = 40 \quad \text{(Equation 2)} \]

### Step 3: Combine the Statements
Now, we have two equations:
1. \(\text{Speed of the boat} - \text{Speed of the water} = 20\) (Equation 1)
2. \(\text{Speed of the boat} + \text{Speed of the water} = 40\) (Equation 2)

- To find the speed of the boat, we can add both equations:
\[ (\text{Speed of the boat} - \text{Speed of the water}) + (\text{Speed of the boat} + \text{Speed of the water}) = 20 + 40 \]
\[ 2 \times \text{Speed of the boat} = 60 \]
\[ \text{Speed of the boat} = 30 \text{ km/h} \]

### Conclusion
Thus, the speed of the boat in still water is **30 km/h**.