Following are the questions based on two statements and answer the following based on the given statements.
A boat covers 35 km in upstream and 35km in downstream in total 4 hours. In what time it will cover 50km upstream?
Statement I. Sum of upstream and downstream speed of the boat is 36km/h
Statement II. Speed of water current is 20% of speed of boat in still water.

Options

A. Statement I alone is sufficient to answer the question while statement II alone is not sufficient to answer the question
B. Statement II alone is sufficient to answer the question while statement I alone is not sufficient to answer the question
C. Both statements I and Il together are required to answer the question.
D. Either the statement I alone or Statement II alone is sufficient to answer the question

Answer

To solve the problem step-by-step, we will analyze the information provided and use the two statements to find the time taken by the boat to cover 50 km upstream.

### Step 1: Understand the Problem
We know that the boat covers 35 km in upstream and 35 km in downstream in a total of 4 hours. We need to find out how long it will take to cover 50 km upstream.

### Step 2: Define Variables
Let:
- \( S_B \) = Speed of the boat in still water (km/h)
- \( S_S \) = Speed of the stream (km/h)

### Step 3: Set Up Equations
From the problem, we can write the time taken for upstream and downstream:
- Time taken upstream = \( \frac{35}{S_B - S_S} \)
- Time taken downstream = \( \frac{35}{S_B + S_S} \)

Since the total time is 4 hours, we can set up the equation:
\[ \frac{35}{S_B - S_S} + \frac{35}{S_B + S_S} = 4 \]

### Step 4: Analyze Statement I
**Statement I:** The sum of upstream and downstream speed of the boat is 36 km/h.
This means:
\[ (S_B - S_S) + (S_B + S_S) = 36 \]
Simplifying this gives:
\[ 2S_B = 36 \implies S_B = 18 \text{ km/h} \]

### Step 5: Substitute \( S_B \) in the Time Equation
Now substituting \( S_B = 18 \) into the time equation:
\[ \frac{35}{18 - S_S} + \frac{35}{18 + S_S} = 4 \]

### Step 6: Solve for \( S_S \)
To solve for \( S_S \), we can multiply through by the common denominator:
\[ 35(18 + S_S) + 35(18 - S_S) = 4(18^2 - S_S^2) \]
This simplifies to:
\[ 1260 = 4(324 - S_S^2) \]
Solving gives:
\[ 1260 = 1296 - 4S_S^2 \implies 4S_S^2 = 36 \implies S_S^2 = 9 \implies S_S = 3 \text{ km/h} \]

### Step 7: Calculate Upstream Speed
Now we can find the upstream speed:
\[ S_B - S_S = 18 - 3 = 15 \text{ km/h} \]

### Step 8: Find Time to Cover 50 km Upstream
Now we can find the time taken to cover 50 km upstream:
\[ \text{Time} = \frac{50}{15} = \frac{10}{3} \text{ hours} \approx 3.33 \text{ hours} \]

### Conclusion
Thus, the time taken to cover 50 km upstream is approximately 3.33 hours.