Shortcut Trick
Ratio of Profit = Σ(Investment × Time)
Simplify investments (divide by 10,000): Sunaina (5), Bhumika (8), Preeti (12)
Ratio S : B : P = (5×4 + 3×8) : (8×4 + 12×8) : (12×4 + 8×8)
Ratio S : B : P = 44 : 128 : 112 ⇒ 11 : 32 : 28 (Total = 71 units)
Preeti's share = (28 ÷ 71) × 1,07,991 = 28 × 1,521 = ₹42,588
∴ The correct answer is ₹42,588.
Alternate Method
Given:
Initial Investments: Sunaina = ₹50,000, Bhumika = ₹80,000, Preeti = ₹1,20,000.
Total time = 12 months. Changes occur after 4 months.
Formula Used:
Profit Ratio = (Capital1 × Time1) + (Capital2 × Time2)
Calculations:
⇒ Sunaina's total investment = (50,000 × 4) + (30,000 × 8) = 2,00,000 + 2,40,000 = 4,40,000
⇒ Bhumika's total investment = (80,000 × 4) + (1,20,000 × 8) = 3,20,000 + 9,60,000 = 12,80,000
⇒ Preeti's total investment = (1,20,000 × 4) + (80,000 × 8) = 4,80,000 + 6,40,000 = 11,20,000
⇒ Ratio of profits = 4,40,000 : 12,80,000 : 11,20,000 = 44 : 128 : 112
⇒ Simplified Ratio = 11 : 32 : 28
⇒ Sum of ratio parts = 11 + 32 + 28 = 71 units
⇒ 71 units = ₹1,07,991
⇒ 1 unit = 1,07,991 ÷ 71 = ₹1,521
⇒ Preeti's share = 28 × 1,521 = ₹42,588
∴ The correct answer is ₹42,588.
Additional Information
Partnership Profit Rule
In a partnership, profit is distributed based on the product of the capital invested and the duration for which it was kept in the business.
Compound Partnership
When partners invest different amounts for different time periods, it is called a compound partnership. Profit Ratio = (C1 × T1) : (C2 × T2) : (C3 × T3).
Working vs Sleeping Partner
A working partner manages the business and may receive an additional salary or commission from the profit before the remaining profit is shared among all partners.