The speed of a boat in still water is 12 km per hour. Going downstream it moves at the rate of 19 km per hour.The speed of the boat against the stream is -----

Options

A. 5 km/hr
B. 3 km/hr
C. 8 km/hr
D. Data inadequate

Answer

To find the speed of the boat against the stream, we can follow these steps:

### Step 1: Identify the given values
- Speed of the boat in still water (x) = 12 km/h
- Speed of the boat downstream (u) = 19 km/h

### Step 2: Set up the equation for downstream speed
The speed of the boat downstream is the sum of the speed of the boat in still water and the speed of the stream (y):
\[ u = x + y \]
Substituting the known values:
\[ 19 = 12 + y \]

### Step 3: Solve for the speed of the stream (y)
To find y, rearrange the equation:
\[ y = 19 - 12 \]
\[ y = 7 \text{ km/h} \]
So, the speed of the stream is 7 km/h.

### Step 4: Set up the equation for upstream speed
The speed of the boat against the stream (v) is the difference between the speed of the boat in still water and the speed of the stream:
\[ v = x - y \]
Substituting the known values:
\[ v = 12 - 7 \]

### Step 5: Calculate the speed of the boat against the stream
Now, calculate v:
\[ v = 5 \text{ km/h} \]

### Final Answer
The speed of the boat against the stream is **5 km/h**.

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