A boat can cover 144 km in downstream and 96 km in upstream in total 12 hours. If ratio of speed of boat in still water to speed of stream is 5:1, then find distance covered by boat in 5 hours in upstream is what percent more than distance covered by boat in 3 hours in downstream?

Options

A. A)`9(1)/(11)%`
B. B)`16(2)/(3)%`
C. C)`11(1)/(9)%`
D. D)`30 %`

Answer

To solve the problem step by step, we will break down the information given and use it to find the required distances and percentages.

### Step 1: Understand the given information
- The boat can cover 144 km downstream and 96 km upstream in a total of 12 hours.
- The ratio of the speed of the boat in still water to the speed of the stream is 5:1.

### Step 2: Define variables
Let:
- Speed of the boat in still water = 5x km/h
- Speed of the stream = x km/h

### Step 3: Calculate effective speeds
- Downstream speed = Speed of boat + Speed of stream = (5x + x) = 6x km/h
- Upstream speed = Speed of boat - Speed of stream = (5x - x) = 4x km/h

### Step 4: Set up the time equations
Using the formula: Time = Distance / Speed

- Time taken to cover 144 km downstream:
\[ \text{Time}_{\text{downstream}} = \frac{144}{6x} \]

- Time taken to cover 96 km upstream:
\[ \text{Time}_{\text{upstream}} = \frac{96}{4x} \]

### Step 5: Set up the total time equation
According to the problem, the total time is 12 hours:
\[ \frac{144}{6x} + \frac{96}{4x} = 12 \]

### Step 6: Simplify the equation
Multiply through by \(12x\) to eliminate the denominators:
\[ 12 \cdot 144 + 12 \cdot 96 = 12 \cdot 6x \cdot 4x \]
\[ 1728 + 1152 = 72x \]
\[ 2880 = 72x \]
\[ x = 40 \text{ km/h} \]

### Step 7: Calculate the speeds
- Speed of the boat in still water = \(5x = 5 \cdot 40 = 200 \text{ km/h}\)
- Speed of the stream = \(x = 40 \text{ km/h}\)

### Step 8: Calculate distances covered in upstream and downstream
- Downstream speed = \(6x = 240 \text{ km/h}\)
- Upstream speed = \(4x = 160 \text{ km/h}\)

### Step 9: Calculate distances in given times
- Distance covered in 5 hours upstream:
\[ \text{Distance}_{\text{upstream}} = \text{Speed}_{\text{upstream}} \times \text{Time} = 160 \text{ km/h} \times 5 \text{ hours} = 800 \text{ km} \]

- Distance covered in 3 hours downstream:
\[ \text{Distance}_{\text{downstream}} = \text{Speed}_{\text{downstream}} \times \text{Time} = 240 \text{ km/h} \times 3 \text{ hours} = 720 \text{ km} \]

### Step 10: Calculate the percentage increase
To find how much more the distance covered in upstream is compared to downstream:
\[ \text{Difference} = 800 - 720 = 80 \text{ km} \]
Percentage increase:
\[ \text{Percentage Increase} = \left(\frac{\text{Difference}}{\text{Distance}_{\text{downstream}}}\right) \times 100 = \left(\frac{80}{720}\right) \times 100 = \frac{8000}{720} \approx 11.11\% \]

### Final Answer
The distance covered by the boat in 5 hours upstream is approximately **11.11% more** than the distance covered in 3 hours downstream.