A, B, and C start a business. B's investment equals one-sixth of the total capital, and A's and C's investments are equal (they split the remaining equally). If the annual profit is ₹ 33,600, find the difference between the profits of B and C.

Introduction / Context: Profit shares are proportional to invested capital when time is equal. If one partner has a specified fraction of the total and the others share the remainder equally, the profit split mirrors those capital fractions.

Given Data / Assumptions:

• Total capital = T.
• B = T/6.
• Remaining capital = 5T/6; A = C = (5T/6)/2 = 5T/12 each.
• Total profit = ₹ 33,600.

Concept / Approach: Convert the fractions into a simple integer ratio for A : B : C and then compute profits. Finally, take the difference between B's and C's profits.

Step-by-Step Solution: Capitals: A = 5T/12, B = T/6, C = 5T/12. Express over a common denominator 12: A = 5, B = 2, C = 5. Profit ratio = 5 : 2 : 5; total parts = 12. Each part = 33,600 / 12 = ₹ 2,800. B's profit = 2 * 2,800 = ₹ 5,600; C's profit = 5 * 2,800 = ₹ 14,000. Difference (C − B) = 14,000 − 5,600 = ₹ 8,400.

Verification / Alternative check: A also earns ₹ 14,000; sum = 14,000 + 5,600 + 14,000 = ₹ 33,600.

Why Other Options Are Wrong: The other differences correspond to incorrect ratios or miscomputations of the per-part profit.

Common Pitfalls: Treating B as 1/3 or sharing the remaining capital incorrectly instead of dividing 5T/6 equally between A and C.

Final Answer: ₹ 8,400