A contractor receives two orders A and B. For order A he spends Rs 25,000 and submits a bill for Rs 30,500. For order B he submits a bill that includes a profit of 20% on his cost. Which of the two orders is more profitable to him?

Introduction / Context:
This problem compares profit percentages on two different contracts taken by a contractor. In real life, contractors often handle several jobs and may earn different profit rates on each. The goal is to identify which order yields the higher profit percentage, not just the higher absolute profit amount.

Given Data / Assumptions:
- For order A: cost = Rs 25,000 and bill (selling price) = Rs 30,500. - For order B: the contractor includes a profit of 20% on cost. - Exact cost of B is not stated, but the profit rate is fixed at 20%. - Profit percentage is calculated as profit divided by cost price, multiplied by 100.

Concept / Approach:
We calculate the profit percentage for order A directly using the known cost and billed amount. For order B we know profit percentage is exactly 20% by definition. Then we simply compare the two percentages to decide which is more profitable.

Step-by-Step Solution:
Step 1: For order A, cost price CA = 25,000 and selling price SA = 30,500. Step 2: Profit on A = SA - CA = 30,500 - 25,000 = Rs 5,500. Step 3: Profit percent on A = (5,500 / 25,000) * 100. Step 4: Compute 5,500 / 25,000 = 0.22, so profit percent on A = 22%. Step 5: For order B, the profit percent is given directly as 20%. Step 6: Compare 22% for A with 20% for B. Since 22% is greater, order A is more profitable.

Verification / Alternative check:
To further verify, assume an example cost for order B, say Rs 10,000. Then the bill amount would be 10,000 * 1.20 = Rs 12,000. Profit would be 2,000, and profit percent would be 2,000 / 10,000 * 100 = 20%, which is less than 22% obtained for order A. Any cost chosen for B gives the same percentage, so the comparison remains valid.

Why Other Options Are Wrong:
Option B (order A) is actually correct. Option A (order B) is wrong because B gives only 20% profit. Option C claiming neither is more profitable is incorrect because 22% is clearly higher than 20%. Option D is also wrong because one of the named orders is definitely more profitable.

Common Pitfalls:
Students might compare only the absolute profit values without thinking in terms of percentages, or assume that B must be better because 20% sounds like a strong profit. The correct approach is always to calculate the actual percentage profit on cost for each order and then compare them.

Final Answer:
Order A is more profitable to the contractor because it yields a 22% profit compared to 20% on order B.