A and B invest ₹ 35,000 and ₹ 20,000, respectively. After 5 months B leaves; C joins with ₹ 15,000 for the remaining 7 months. If the profit at year end is ₹ 84,125, what is B's share?

Introduction / Context: Unequal durations require capital-time weighting. Compute each partner's weight and then allocate profit exactly proportional to these weights.

Given Data / Assumptions:

• A: 35,000 for 12 months.
• B: 20,000 for 5 months.
• C: 15,000 for 7 months.
• Total profit = ₹ 84,125.

Concept / Approach: Form weights, reduce to an integer ratio, then multiply by per-part profit to find B's share.

Step-by-Step Solution: A's weight = 35,000*12 = 4,20,000. B's weight = 20,000*5 = 1,00,000. C's weight = 15,000*7 = 1,05,000. Ratio = 84 : 20 : 21 (dividing by 5,000). Total parts = 125; per part = 84,125 / 125 = ₹ 673. B's share = 20 * 673 = ₹ 13,460.

Verification / Alternative check: A's share = 84 * 673 = ₹ 56,532; C's share = 21 * 673 = ₹ 14,133; sum equals ₹ 84,125.

Why Other Options Are Wrong: ₹ 14,133 belongs to C. ₹ 15,000 or ₹ 12,800 are not integer multiples of ₹ 673 with part count 20.

Common Pitfalls: Rounding the per-part value prematurely or mishandling months for B and C.

Final Answer: ₹ 13,460