A boat can row 10 km in 5/6th of an hour in down stream and12 km in upstream in 90 minutes. Find the speed of stream and speed of boat in still water.(in kmph)

Options

A. 12,2
B. 16,4
C. 4,8
D. 2,10

Answer

To solve the problem, we will first determine the speed of the boat in still water (x) and the speed of the stream (y) using the information provided.

### Step 1: Calculate the speed of the boat downstream
The distance covered downstream is 10 km, and the time taken is \( \frac{5}{6} \) hours.

Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Substituting the values:
\[ \text{Speed downstream} = \frac{10 \text{ km}}{\frac{5}{6} \text{ hours}} = 10 \times \frac{6}{5} = 12 \text{ km/h} \]
This speed can be expressed as:
\[ x + y = 12 \quad \text{(1)} \]

### Step 2: Calculate the speed of the boat upstream
The distance covered upstream is 12 km, and the time taken is 90 minutes, which is \( \frac{90}{60} = 1.5 \) hours.

Using the formula for speed again:
\[ \text{Speed upstream} = \frac{12 \text{ km}}{1.5 \text{ hours}} = 8 \text{ km/h} \]
This speed can be expressed as:
\[ x - y = 8 \quad \text{(2)} \]

### Step 3: Solve the equations
Now we have two equations:
1. \( x + y = 12 \)
2. \( x - y = 8 \)

We can add these two equations to eliminate y:
\[ (x + y) + (x - y) = 12 + 8 \]
This simplifies to:
\[ 2x = 20 \implies x = 10 \text{ km/h} \]

### Step 4: Find the speed of the stream
Now that we have the value of x (speed of the boat in still water), we can substitute it back into one of the equations to find y. Let's use equation (1):
\[ 10 + y = 12 \implies y = 12 - 10 = 2 \text{ km/h} \]

### Final Answer
The speed of the boat in still water is **10 km/h** and the speed of the stream is **2 km/h**.

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