What is the speed of boat?
(A) Sum of time taken by a boat in upstream and downstream is 18 hours to cover distance 180 km in each.
(B) Speed of boat in downstream is 30 km/ h.
(C ) Boat cover 90 km in 7 hr, while rowing in upstream

Options

A. Either A and B or B and C are sufficient to answer the question
B. Either A and B or A and C are sufficient to answer the question
C. Either A and C or B and C are sufficient to answer the question
D. Any two statements are sufficient to answer the question

Explanation

To find the speed of the boat, we will analyze the given statements step by step.

### Step 1: Understand the Problem
We need to find the speed of the boat. We have three statements that provide information about the boat's journey upstream and downstream.

### Step 2: Analyze Statement (A)
Statement (A) states that the sum of the time taken by the boat in upstream and downstream is 18 hours to cover a distance of 180 km in each direction.

- Let the speed of the boat in still water be \( x \) km/h and the speed of the stream be \( y \) km/h.
- The time taken to travel upstream (against the current) is given by:
\[ \text{Time}_{\text{upstream}} = \frac{180}{x - y} \]
- The time taken to travel downstream (with the current) is given by:
\[ \text{Time}_{\text{downstream}} = \frac{180}{x + y} \]
- According to statement (A):
\[ \frac{180}{x - y} + \frac{180}{x + y} = 18 \]
- This equation gives us a relationship between \( x \) and \( y \).

### Step 3: Analyze Statement (B)
Statement (B) states that the speed of the boat in downstream is 30 km/h.

- From this, we have:
\[ x + y = 30 \]
- This gives us another equation involving \( x \) and \( y \).

### Step 4: Analyze Statement (C)
Statement (C) states that the boat covers 90 km in 7 hours while rowing upstream.

- The speed while rowing upstream is:
\[ \text{Speed}_{\text{upstream}} = \frac{90}{7} \text{ km/h} \]
- This can be expressed as:
\[ x - y = \frac{90}{7} \]

### Step 5: Combine the Statements
Now we have three equations:
1. From statement (A):
\[ \frac{180}{x - y} + \frac{180}{x + y} = 18 \]
2. From statement (B):
\[ x + y = 30 \]
3. From statement (C):
\[ x - y = \frac{90}{7} \]

We can solve these equations to find \( x \) (the speed of the boat).

### Step 6: Solve the Equations
Using equations from statements (B) and (C):
1. \( x + y = 30 \)
2. \( x - y = \frac{90}{7} \)

Adding these two equations:
\[ (x + y) + (x - y) = 30 + \frac{90}{7} \]
\[ 2x = 30 + \frac{90}{7} \]
To combine, convert 30 into a fraction:
\[ 30 = \frac{210}{7} \]
So,
\[ 2x = \frac{210}{7} + \frac{90}{7} = \frac{300}{7} \]
Thus,
\[ x = \frac{150}{7} \text{ km/h} \]

### Step 7: Conclusion
The speed of the boat is \( \frac{150}{7} \approx 21.43 \text{ km/h} \).