A driver of auto rickshaw makes a profit of 20% on every trip when he carries 3 passengers and the price of petrol is Rs. 30 a litre. Find the % profit for the same journey if he goes for 4 passengers per trip and the price of petrol reduces to Rs. 24 litres ?

Options

A. A. 55%
B. B. 100%
C. C. 120%
D. D. 98%

Explanation

To solve the problem, we need to find the percentage profit for the auto rickshaw driver when he carries 4 passengers and the price of petrol reduces to Rs. 24 per litre. Let's break down the solution step by step.

### Step 1: Determine the cost price (CP) when carrying 3 passengers.
Given that the driver makes a profit of 20% when carrying 3 passengers, we can denote:
- Selling Price (SP) = CP + Profit
- Profit = 20% of CP = 0.20 * CP

Let’s assume the cost price (CP) for the trip when carrying 3 passengers is Rs. 100 (this is just an assumption to simplify calculations).

Then, the profit when carrying 3 passengers would be:
Profit = 0.20 * 100 = Rs. 20

So, the Selling Price (SP) when carrying 3 passengers would be:
SP = CP + Profit = 100 + 20 = Rs. 120

### Step 2: Calculate the total revenue from carrying 3 passengers.
If the driver carries 3 passengers and earns Rs. 120, the revenue per passenger would be:
Revenue per passenger = Total Revenue / Number of Passengers
Revenue per passenger = 120 / 3 = Rs. 40

### Step 3: Calculate the cost of petrol for the trip when carrying 4 passengers.
Now, we need to find the cost of petrol when carrying 4 passengers. The cost of petrol is Rs. 24 per litre. Let’s assume the distance covered is the same as when carrying 3 passengers.

Let’s say the distance requires 2 litres of petrol (again, this is an assumption for calculation purposes).

Total cost of petrol = Price per litre * Quantity of petrol
Total cost of petrol = 24 * 2 = Rs. 48

### Step 4: Calculate the total revenue from carrying 4 passengers.
If the driver carries 4 passengers, the total revenue would be:
Total Revenue = Revenue per passenger * Number of Passengers
Total Revenue = 40 * 4 = Rs. 160

### Step 5: Calculate the profit when carrying 4 passengers.
Now, we can calculate the profit when carrying 4 passengers:
Profit = Total Revenue - Total Cost
Profit = 160 - 48 = Rs. 112

### Step 6: Calculate the percentage profit when carrying 4 passengers.
Percentage Profit = (Profit / Total Cost) * 100
Total Cost when carrying 4 passengers = Cost of petrol = Rs. 48

Percentage Profit = (112 / 48) * 100 ≈ 233.33%

### Final Answer:
The percentage profit when carrying 4 passengers and the price of petrol is Rs. 24 per litre is approximately 233.33%.

---