Read the given information carefully and answer the following questions. A boat covers certain distance 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. How much fuel is consumed in covering downstream distance in whole journey? (approx.)

Options

A. 15 lit
B. 17 lit
C. 18 lit
D. 12 lit

Answer

To solve the problem step by step, we will break down the information provided and calculate the fuel consumed in covering the downstream distance during the entire journey.

### Step 1: Understand the Ratios and Distances
We know the ratio of distances covered downstream to upstream is 7:3. The total distance covered is 375 km, and the distance covered in still water is 175 km.

**Calculation:**
- Let the distance covered downstream be \(7x\) and upstream be \(3x\).
- The total distance covered in downstream and upstream is \(7x + 3x = 10x\).
- Given that the total distance covered is 375 km, we have:
\[ 10x + 175 = 375 \]
\[ 10x = 375 - 175 = 200 \]
\[ x = 20 \]
- Therefore, the distances are:
- Downstream: \(7x = 7 \times 20 = 140 \text{ km}\)
- Upstream: \(3x = 3 \times 20 = 60 \text{ km}\)

**Hint:** Use the ratio to express distances in terms of a variable and solve for that variable using the total distance.

### Step 2: Calculate Fuel Consumption Rates
Let the fuel consumed in still water be \(X\) liters per km.

- **Downstream Consumption:** 25% less fuel means:
\[ \text{Fuel per km downstream} = X \times (1 - 0.25) = 0.75X \]

- **Upstream Consumption:** 12.5% more fuel means:
\[ \text{Fuel per km upstream} = X \times (1 + 0.125) = 1.125X \]

**Hint:** Adjust the fuel consumption rates based on the percentage increase or decrease as given in the problem.

### Step 3: Calculate Fuel Consumption for the Initial Journey
Now, we calculate the total fuel consumed during the initial journey.

- **Fuel consumed downstream:**
\[ \text{Fuel downstream} = 140 \text{ km} \times 0.75X = 105X \]

- **Fuel consumed upstream:**
\[ \text{Fuel upstream} = 60 \text{ km} \times 1.125X = 67.5X \]

- **Fuel consumed in still water:**
\[ \text{Fuel in still water} = 175 \text{ km} \times X = 175X \]

- **Total fuel consumed in the initial journey:**
\[ \text{Total fuel} = 105X + 67.5X + 175X = 347.5X \]

**Hint:** Break down the journey into segments and calculate the fuel for each segment separately.

### Step 4: Calculate Fuel Consumption for the Return Journey
During the return journey, the distances are reversed:
- Downstream becomes upstream (60 km)
- Upstream becomes downstream (140 km)

- **Fuel consumed downstream (now upstream):**
\[ \text{Fuel upstream} = 60 \text{ km} \times 1.125X = 67.5X \]

- **Fuel consumed upstream (now downstream):**
\[ \text{Fuel downstream} = 140 \text{ km} \times 0.75X = 105X \]

- **Fuel consumed in still water remains the same:**
\[ \text{Fuel in still water} = 175X \]

- **Total fuel consumed in the return journey:**
\[ \text{Total fuel} = 67.5X + 105X + 175X = 347.5X \]

**Hint:** Remember that the distances for downstream and upstream switch in the return journey.

### Step 5: Account for Additional Fuel Consumption
The problem states that the return journey takes an additional \(\frac{10}{3}\) liters of fuel.

Setting up the equation:
\[ 347.5X + \frac{10}{3} = 347.5X \]

This implies that the total fuel consumed for both journeys must equal:
\[ 347.5X + \frac{10}{3} = 377.5X \]

**Hint:** Set up an equation to relate the total fuel consumed in both journeys.

### Step 6: Solve for \(X\)
From the equation:
\[ \frac{10}{3} = 377.5X - 347.5X \]
\[ \frac{10}{3} = 30X \]
\[ X = \frac{10}{90} = \frac{1}{9} \text{ liters/km} \]

**Hint:** Isolate \(X\) to find the fuel consumption rate in still water.

### Step 7: Calculate Fuel Consumed in Downstream Distance
Now, we can calculate the fuel consumed in covering the downstream distance during the entire journey.

- **Fuel consumed downstream (initial journey):**
\[ \text{Fuel downstream} = 140 \text{ km} \times 0.75X = 140 \times 0.75 \times \frac{1}{9} = \frac{105}{9} \approx 11.67 \text{ liters} \]

- **Fuel consumed downstream (return journey):**
\[ \text{Fuel downstream} = 60 \text{ km} \times 0.75X = 60 \times 0.75 \times \frac{1}{9} = \frac{45}{9} \approx 5 \text{ liters} \]

- **Total fuel consumed downstream:**
\[ \text{Total downstream fuel} = 11.67 + 5 \approx 16.67 \text{ liters} \]

**Final Answer:**
The total fuel consumed in covering the downstream distance in the whole journey is approximately **17 liters**.