If A, B and C enter into a partnership with shares in the ratio 7/2:4/3:6/5.…

Concept: When two or more partners keep different amounts of capital invested for different lengths of time within the same year, profit is divided in the ratio of each partner's capital multiplied by the number of months it stayed invested, not in the plain capital ratio. A partner who changes their investment partway through the year contributes at each capital level for that level's own duration.

Applying it here:

1. Simplify the given ratio 7/2 : 4/3 : 6/5 to a whole-number ratio by multiplying each term by the LCM of the denominators 2, 3 and 5, which is 30: (7/2)×30 : (4/3)×30 : (6/5)×30 = 105 : 40 : 36. Let A, B and C's capitals be 105k, 40k and 36k.

2. A's capital stays at 105k for the first 4 months, then rises by 50% to 105k × 1.5 = 157.5k for the remaining 8 months. B's and C's capitals stay unchanged for all 12 months.

3. Compute each partner's capital-months: A = 105k × 4 + 157.5k × 8 = 420k + 1260k = 1680k; B = 40k × 12 = 480k; C = 36k × 12 = 432k.

4. Add the capital-months to get the profit-sharing ratio: 1680k : 480k : 432k, which simplifies (divide by 48k) to 35 : 10 : 9, totaling 54 parts.

5. B's share of the Rs. 21,600 profit = (10/54) × 21,600 = Rs. 4,000.

Cross-check: Verifying the split across all three partners:

• A's share = (35/54) × 21,600 = Rs. 14,000

• B's share = (10/54) × 21,600 = Rs. 4,000

• C's share = (9/54) × 21,600 = Rs. 3,600

Together, 14,000 + 4,000 + 3,600 = Rs. 21,600, which matches the given total profit exactly, confirming B's share of Rs. 4,000.