A, B and C subscribe a total capital of Rs. 50,000 for a business. A contributes Rs. 4,000 more than B, and B contributes Rs. 5,000 more than C. Out of a total profit of Rs. 35,000, how much does A receive?

Introduction / Context:
This question combines algebra with the partnership concept. Three partners A, B and C contribute a total of Rs. 50,000, with known differences between their capital amounts. We must first determine the individual capitals by forming equations, and then use these amounts to divide a total profit of Rs. 35,000 in the correct ratio and find A's share.

Given Data / Assumptions:

• Total capital subscribed by A, B and C is Rs. 50,000.
• A contributes Rs. 4,000 more than B.
• B contributes Rs. 5,000 more than C.
• Total profit at the end of the period is Rs. 35,000.
• All three partners keep their capital invested for the same time period.
• Profit is shared in proportion to their respective capital contributions.

Concept / Approach:
First we use the differences between the capitals and the total capital to set up algebraic equations and solve for the individual capital amounts. Once the capitals of A, B and C are known, we find the ratio A : B : C and apply it to the given total profit. The concept is straightforward partnership based on capital only, since time is assumed to be equal for all.

Step-by-Step Solution:
Step 1: Let C's capital be c rupees. Step 2: B contributes Rs. 5,000 more than C, so B's capital = c + 5,000. Step 3: A contributes Rs. 4,000 more than B, so A's capital = (c + 5,000) + 4,000 = c + 9,000. Step 4: The total capital is A + B + C = (c + 9,000) + (c + 5,000) + c = 3c + 14,000 = 50,000. Step 5: Solve for c: 3c + 14,000 = 50,000 implies 3c = 36,000, so c = 12,000. Step 6: Then B's capital = 12,000 + 5,000 = 17,000 and A's capital = 12,000 + 9,000 = 21,000. Step 7: The capital ratio A : B : C = 21,000 : 17,000 : 12,000. Divide all by 1,000 to get 21 : 17 : 12. Step 8: Total ratio parts = 21 + 17 + 12 = 50. Step 9: Profit per part = 35,000 / 50 = 700. Step 10: A's share = 21 parts = 21 * 700 = Rs. 14,700.

Verification / Alternative check:
Compute B's and C's shares using the same ratio. B gets 17 * 700 = 11,900 and C gets 12 * 700 = 8,400. Adding them together gives 14,700 + 11,900 + 8,400 = 35,000, matching the total profit. The capital ratio and profit distribution are therefore consistent with all given conditions.

Why Other Options Are Wrong:
If A were to receive Rs. 15,000, Rs. 12,000 or Rs. 13,500, then the remaining profit would not divide between B and C in the ratio 17 : 12. The sum of individual shares also would not match the required proportions based on capitals of 21,000, 17,000 and 12,000. Thus those options are not compatible with the established capital ratio.

Common Pitfalls:
Common errors include incorrectly forming the total capital equation, for example by misplacing the 4,000 and 5,000 differences, or forgetting that the total capital is 50,000. Another mistake is simplifying the ratio incorrectly, which then leads to wrong profit shares. Taking care with the algebraic steps and rechecking the final sum of shares helps avoid such mistakes.

Final Answer:
A receives a profit share of Rs. 14,700.