Read the given information carefully and answer the following questions.
A boat covers certain distance of it's journey in three parts i.e. upstream, downstream and in still water. Ratio of distance covered in downstream to upstream is 7:3 and total distance covered is 375 km. When boat goes downstream it consume 25% less fuel per km and while moving in upstream it consumes `12(1)/(2)%` more fuel per km than that of in still water and it cover 175km in still water. Now, after reaching its destination, boat returns to initial point covering the same path and it takes `(10)/(3)` lit more fuel in return journey.
If in return journey boat takes 5hr 30 min more to cover upstream than downstream and speed of boat in downstream is 40km/h, then find speed of boat in upstream?

Options

A. 10 km/h
B. 15 km/h
C. 20 km/h
D. 25 km/h

Answer

To solve the problem step by step, we will break down the information provided and calculate the required speed of the boat in upstream.

### Step 1: Understand the Distances
The total distance covered by the boat is 375 km. The distances covered in downstream (D) and upstream (U) are in the ratio 7:3.

Let the distance covered downstream be \(7x\) and the distance covered upstream be \(3x\).

From the ratio:
\[ D + U + \text{Distance in still water} = 375 \]
Given that the distance in still water is 175 km, we can write:
\[ 7x + 3x + 175 = 375 \]
This simplifies to:
\[ 10x + 175 = 375 \]
Subtracting 175 from both sides gives:
\[ 10x = 200 \]
So,
\[ x = 20 \]

Now we can find the distances:
\[ D = 7x = 7 \times 20 = 140 \text{ km (downstream)} \]
\[ U = 3x = 3 \times 20 = 60 \text{ km (upstream)} \]

### Step 2: Calculate Time Taken for Downstream
The speed of the boat in downstream is given as 40 km/h. The time taken to cover the downstream distance can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Thus,
\[ \text{Time for downstream} = \frac{140 \text{ km}}{40 \text{ km/h}} = 3.5 \text{ hours} \]

### Step 3: Calculate Time Taken for Upstream
Let the speed of the boat in upstream be \(v\) km/h. The time taken to cover the upstream distance is:
\[ \text{Time for upstream} = \frac{60 \text{ km}}{v \text{ km/h}} \]

### Step 4: Set Up the Equation for Time Difference
According to the problem, the time taken for upstream is 5 hours and 30 minutes more than the time taken for downstream:
\[ \frac{60}{v} = 3.5 + 5.5 \]
Converting 5 hours and 30 minutes to hours gives us:
\[ 5.5 \text{ hours} \]
Thus, we can write:
\[ \frac{60}{v} = 9 \]

### Step 5: Solve for Upstream Speed
Now, we can solve for \(v\):
\[ 60 = 9v \]
\[ v = \frac{60}{9} = \frac{20}{3} \approx 20 \text{ km/h} \]

### Conclusion
The speed of the boat in upstream is approximately \(20\) km/h.

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