Consumption of fuel by car varies exponentially with respect to speed. When a car travels at a speed of 100 kmph, it uses 25% more petrol to travel a certain distance than it does when it travels at a speed of 75 kmph. If the mileage of the car is 25 kmpl at a speed of 75 kmph, then what can be the amount of petrol required (in liters) to travel a distance of 225 km in 150 minutes?

To solve this problem, we need to find the amount of petrol required to travel 225 km given the conditions. Here's a step-by-step breakdown of the solution:

### Step 1: Understanding the Problem
- The car's fuel consumption varies exponentially with speed.
- At 75 kmph, the car has a mileage of 25 km per liter (kmpl).
- At 100 kmph, the car uses 25% more petrol compared to 75 kmph.

### Step 2: Calculate Mileage at 100 kmph
Given that the car uses 25% more petrol at 100 kmph than at 75 kmph:
- Let \( M_{75} \) be the mileage at 75 kmph, which is 25 kmpl.
- The additional petrol consumption at 100 kmph is 25%, so the effective mileage decreases.

The factor of increased consumption is \( 1 + 0.25 = 1.25 \).

New mileage \( M_{100} \) can be calculated as:
\[
M_{100} = \frac{M_{75}}{1.25} = \frac{25}{1.25} = 20 \text{ kmpl}
\]

### Step 3: Determine the Speed and Time
We need to find the amount of petrol required to travel 225 km in 150 minutes.

Convert the time to hours:
\[
150 \text{ minutes} = \frac{150}{60} = 2.5 \text{ hours}
\]

Now, calculate the speed:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{225 \text{ km}}{2.5 \text{ hours}} = 90 \text{ kmph}
\]

### Step 4: Estimate the Mileage at 90 kmph
Since mileage decreases exponentially, and we know the values at 75 kmph and 100 kmph, we can interpolate or estimate the mileage at 90 kmph. 

Since 90 kmph is closer to 100 kmph, the mileage will be slightly better than 20 kmpl but less than 25 kmpl. To approximate, we can use a linear estimation (as an exponential model fit could require more specific data points):

Average the mileage between 75 kmph and 100 kmph:
\[
M_{90} \approx \frac{25 + 20}{2} = 22.5 \text{ kmpl}
\]

### Step 5: Calculate the Petrol Required
Finally, calculate the amount of petrol needed for 225 km at an estimated mileage of 22.5 kmpl:
\[
\text{Petrol required} = \frac{\text{Distance}}{\text{Mileage}} = \frac{225}{22.5} = 10 \text{ liters}
\]

So, the amount of petrol required is approximately **10 liters**.

Would you like further details or have any questions?

### Related Questions:
1. How would the petrol requirement change if the distance was increased to 300 km with the same speed and time constraints?
2. What is the impact of exponential variations in fuel consumption on long-distance travel efficiency?
3. How can we more accurately model fuel consumption variations if given additional speed vs. mileage data points?
4. What would the fuel requirement be if the speed was decreased to 80 kmph while keeping the distance constant?
5. How can advanced vehicle technologies help in reducing exponential fuel consumption?

**Tip:** Exponential variations can significantly affect fuel consumption at higher speeds, emphasizing the importance of optimizing driving speed for better fuel efficiency.

Learn how to calculate the amount of petrol required to travel 225 km in 150 minutes using exponential fuel consumption models and interpolation. Understand how speed affects mileage and petrol consumption in cars. Suitable for advanced high school students.

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