A, B, and C invest in a business in the ratio 2:3:5. After 4 months, A increases his capital by 50%, B decreases his capital by 1…

Question

A, B, and C invest in a business in the ratio 2:3:5. After 4 months, A increases his capital by 50%, B decreases his capital by 1/3, and C leaves the capital unchanged. At the end of the year, if the total profit is Rs. 33,000, find the share of B.

1. A. Rs. 8,000
2. B. Rs. 10,500
3. C. Rs. 9,000
4. D. Rs. 7,700 (Correct answer)

Correct Answer

Option D — Rs. 7,700

Detailed Solution & Explanation

The correct answer is Rs. 7,700.

Key Points

• Profit divides in the ratio of capital × time, and each partner's capital changes after 4 months, so split the year into 4 months and 8 months.
• Take the starting capitals as 2, 3 and 5:
  • A: 2×4 + (2 × 1.5)×8 = 8 + 24 = 32
  • B: 3×4 + (3 × 2/3)×8 = 12 + 16 = 28
  • C: 5×12 = 60 (unchanged all year)
• Ratio A : B : C = 32 : 28 : 60 = 8 : 7 : 15, totalling 30 parts.
• B's share = (7/30) × 33,000 = Rs. 7,700.

Additional Information

• "Increases by 50%" means multiplying by 1.5; "decreases by 1/3" means multiplying by 2/3 — the fraction is of the existing capital, not of the original ratio total.
• Check the arithmetic: one part = 33,000/30 = 1,100, so A gets 8,800, B gets 7,700 and C gets 16,500, which sum to 33,000 ✓.
• Where a partner joins or leaves mid-year, the same method applies — break the year at every change and sum capital × months for each interval.
• A working partner takes a salary or commission off the top before this division; a sleeping partner shares strictly by capital and time.