Boat A travel downstream from point X to point Y in 3 hours less than time taken by boat B to travel upstream point Y to Z distance between X and Y is 20 km which is half of the distance between Y and Z ,the speed of boat B in still water is 10 kmph and speed of boat A in still water is equal to the speed of boat B upstream, what is speed of A in still water consider the speed of current to be same

Options

A. 10km/hr
B. 16km/hr
C. 12km/hr
D. 8km/hr

Answer

To solve the problem step by step, we can follow the reasoning provided in the video transcript. Here’s the structured solution:

### Step 1: Identify the distances
- The distance from point X to point Y is given as 20 km.
- The distance from point Y to point Z is double that of X to Y, so it is 40 km.

### Step 2: Define the speeds
- Let the speed of the current (stream) be denoted as \( c \) km/h.
- The speed of boat B in still water is given as 10 km/h.
- The speed of boat A in still water is equal to the speed of boat B upstream. Therefore, the speed of boat A in still water is also \( 10 - c \) km/h (since upstream speed is reduced by the speed of the current).

### Step 3: Calculate the time taken by both boats
- **Time taken by Boat A (downstream from X to Y):**
- Speed downstream = Speed of A + Speed of current = \( (10 - c) + c = 10 \) km/h.
- Time taken = Distance / Speed = \( 20 / 10 = 2 \) hours.

- **Time taken by Boat B (upstream from Y to Z):**
- Speed upstream = Speed of B - Speed of current = \( 10 - c \) km/h.
- Time taken = Distance / Speed = \( 40 / (10 - c) \).

### Step 4: Set up the equation based on the time difference
According to the problem, Boat A takes 3 hours less than Boat B:
\[ 2 = \frac{40}{10 - c} - 3 \]

### Step 5: Solve the equation
1. Rearranging the equation:
\[ \frac{40}{10 - c} = 5 \]
2. Cross-multiplying gives:
\[ 40 = 5(10 - c) \]
3. Expanding and simplifying:
\[ 40 = 50 - 5c \]
\[ 5c = 50 - 40 \]
\[ 5c = 10 \]
\[ c = 2 \text{ km/h} \]

### Step 6: Find the speed of Boat A in still water
- The speed of Boat A in still water is:
\[ 10 - c = 10 - 2 = 8 \text{ km/h} \]

### Final Answer
The speed of Boat A in still water is **8 km/h**.

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