Aman can go downstream thrice as fast as he can go upstream between two specific points on a river. If the river flows at 8 kmph, what is the speed of the boat in still water (in kmph)?

Question

Accepted Answer

Let the speed of the boat in still water be $$ x $$ kmph.

#### Step 1: Define Downstream and Upstream Speeds
- **Downstream speed**: $$ x + 8 $$ kmph (speed of boat + speed of river).  
- **Upstream speed**: $$ x - 8 $$ kmph (speed of boat - speed of river).

#### Step 2: Relation Between Downstream and Upstream Speeds
It is given that the downstream speed is **three times** the upstream speed:  
$$
x + 8 = 3(x - 8).
$$

#### Step 3: Solve the Equation
Expand and simplify:  
$$
x + 8 = 3x - 24.
$$  
Rearrange terms:  
$$
x - 3x = -24 - 8.
$$  
$$
-2x = -32 \implies x = \frac{-32}{-2} = 16.
$$

#### Step 4: Verify the Answer
The speed of the boat in still water is **16 kmph**.

Thus, the correct answer is **3. 16 kmph**.

Answer

Answer

Answer