A driver of an auto rickshaw makes a profit of 20% on every trip when he carries 3 passengers and the petrol price is Rs 30 per litre. For the same journey, if he carries 4 passengers per trip and the petrol price falls to Rs 24 per litre, what percentage profit does he now make, assuming other costs remain unchanged?

Introduction / Context:
This question tests combined reasoning with profit, cost and proportional changes in price and number of passengers. The auto rickshaw driver earns profit from passenger fares while spending money on petrol and other fixed expenses. When the petrol price changes and the number of passengers changes, the profitability of each trip also changes. We need to quantify this change in terms of profit percentage.

Given Data / Assumptions:

• With 3 passengers and petrol at Rs 30 per litre, profit per trip is 20%.
• For the same journey, he later carries 4 passengers.
• Petrol price falls from Rs 30 to Rs 24 per litre (a 20% reduction).
• Other expenses per trip such as maintenance and driver time remain constant.
• Assume the fare charged per passenger for the trip remains unchanged.

Concept / Approach:
We assume that the entire variable cost is petrol, so when petrol price falls by 20%, total trip cost falls by 20%. Let fare per passenger be R. We can then express cost and revenue algebraically for both scenarios. Once we have new revenue and new cost in terms of R, we compute profit% = (profit / cost) * 100. Using algebra with a dummy variable keeps the solution general and clear.

Step-by-Step Solution:
Step 1: Let fare per passenger = R. For 3 passengers, revenue SP₁ = 3R.Step 2: Profit is 20%, so cost C₁ satisfies SP₁ = 1.2 * C₁ ⇒ 3R = 1.2 * C₁ ⇒ C₁ = 3R / 1.2 = 2.5R.Step 3: Petrol price falls by 20%, so new cost C₂ = 0.8 * C₁ = 0.8 * 2.5R = 2R (assuming cost is dominated by petrol).Step 4: With 4 passengers at same fare, new revenue SP₂ = 4R.Step 5: New profit = SP₂ - C₂ = 4R - 2R = 2R, so profit% = (2R / 2R) * 100 = 100%.

Verification / Alternative check:
You may take a concrete value, for example R = Rs 100. Then initially SP₁ = Rs 300 and C₁ = Rs 250, giving 20% profit. After the change, C₂ = Rs 200 and SP₂ = Rs 400, making profit = Rs 200. The profit percentage is (200 / 200) * 100 = 100%. This confirms the algebraic solution and shows that the profit has doubled relative to cost.

Why Other Options Are Wrong:
68%, 80% and 75% might appear realistic but they all underestimate the strong effect of both reduced petrol price and an extra passenger. When you work out the precise algebra, only 100% fits the combined impact of reduced cost and increased revenue. The other values come from partial adjustments or from incorrectly assuming that only one variable (either passengers or petrol price) changes.

Common Pitfalls:
One common error is to treat profit percentage as directly proportional to the number of passengers, ignoring the change in cost. Another is to reduce selling price proportionally with petrol price instead of keeping the fare per passenger fixed. Carefully separating revenue and cost, and writing explicit equations, helps avoid these mistakes in multi-factor percentage questions.

Final Answer:
After carrying 4 passengers and with a reduced petrol price, the driver earns a profit of 100% on the cost of the journey.