Speeds of a boat along the current and against the current are 10 km/hr and 8 km /hr respectively . What is the speed (in km/hr ) of the current ?

Options

A. 1
B. 2
C. 3
D. 9

Answer

To find the speed of the current based on the given speeds of the boat, we can follow these steps:

### Step 1: Understand the terms
- **Downstream speed** (with the current) = 10 km/hr
- **Upstream speed** (against the current) = 8 km/hr

### Step 2: Set up the equations
Let the speed of the boat in still water be \( b \) km/hr and the speed of the current be \( c \) km/hr.
From the definitions:
- Downstream speed = \( b + c \)
- Upstream speed = \( b - c \)

### Step 3: Write the equations based on the problem
From the problem, we have:
1. \( b + c = 10 \) (1)
2. \( b - c = 8 \) (2)

### Step 4: Solve the equations
To find \( b \) and \( c \), we can add equations (1) and (2):
\[ (b + c) + (b - c) = 10 + 8 \]
This simplifies to:
\[ 2b = 18 \]
So,
\[ b = 9 \text{ km/hr} \]

Now, substitute \( b \) back into one of the original equations to find \( c \). We can use equation (1):
\[ 9 + c = 10 \]
Thus,
\[ c = 10 - 9 = 1 \text{ km/hr} \]

### Conclusion
The speed of the current is \( 1 \) km/hr.

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