A trader buys an item for Rs 30 and sells it for Rs 50. What is his profit percentage on this transaction?

Introduction / Context:
This is a straightforward profit percentage question where both cost price and selling price are explicitly given. Such questions verify whether you remember the correct formula for profit% and can apply it accurately without mixing up the numerator and denominator. Even though the numbers are simple, careless mistakes are common in timed exams.

Given Data / Assumptions:

• Cost price (CP) of the item = Rs 30.
• Selling price (SP) of the item = Rs 50.
• There are no additional costs or taxes.
• We must find the percentage profit earned by the trader.

Concept / Approach:
Profit is defined as the difference between selling price and cost price. Profit percentage is always calculated on the cost price unless stated otherwise. The formula is: profit% = (SP - CP) / CP * 100. Once the profit amount is known, we simply divide by CP and convert to a percentage. This basic ratio concept is fundamental to all profit and loss questions.

Step-by-Step Solution:
Step 1: Identify CP = 30 and SP = 50.Step 2: Compute profit = SP - CP = 50 - 30 = 20.Step 3: Use the formula profit% = (profit / CP) * 100.Step 4: Profit% = (20 / 30) * 100.Step 5: 20 / 30 = 2 / 3 ≈ 0.6667, so profit% ≈ 66.67%.

Verification / Alternative check:
If the trader gains 66.67% on a cost price of Rs 30, the selling price should be CP * (1 + 66.67/100) = 30 * (1 + 2/3) = 30 * 5/3 = 50. This matches the actual selling price, confirming that the computed profit percentage is correct. Any other percentage would not convert back to the exact selling price of Rs 50 when multiplied with the cost price.

Why Other Options Are Wrong:
40%, 45% and 35% all represent profit amounts that are too small for an increase from Rs 30 to Rs 50. For example, a 40% profit would correspond to a selling price of 30 * 1.4 = 42, not 50. The difference between SP and CP here is quite large relative to the base, so the correct percentage must also be relatively large, which is captured by 66.67% and not by the smaller options.

Common Pitfalls:
A common mistake is to divide the profit by the selling price instead of the cost price or to incorrectly compute 20/30 as 20/50. Another pitfall is to misinterpret the percentage as 50/30 * 100. Always remember that profit percentage is based on cost price, and carefully place values into the formula to avoid such arithmetic errors.

Final Answer:
The trader earns a profit of approximately 66.67% on the item.