Shortcut Trick Profit ratio = (Capital of X × Time) : (Capital of Y × Time) : (Capital of Z × Time) Profit ratio = (4000 × 3) : (6000 × 2) : (8000 × 4) = 12 : 12 : 32 = 3 : 3 : 8 Total profit ratio = 3 + 3 + 8 = 14 parts. Share of Y = (3 ÷ 14) × 56000 = Rs. 12000 ∴ The correct answer is Rs. 12,000. Alternate Method Given: X's investment = Rs. 4,000 for 3 years Y's investment = Rs. 6,000 for 2 years Z's investment = Rs. 8,000 for 4 years Total profit = Rs. 56,000 Formula Used: Profit Ratio = P_(1) : P_(2) : P_(3) = (C_(1) × T_(1)) : (C_(2) × T_(2)) : (C_(3) × T_(3)) X 4000 × 3 yrs Y 6000 × 2 yrs Z 8000 × 4 yrs Profit Ratio → 12 : 12 : 32 = 3 : 3 : 8 Total Parts = 14 ⇒ Total Profit = Rs. 56,000 Y's Share = 3/14 × 56000 = Rs. 12,000 Calculations: ⇒ Profit Ratio = (4000 × 3) : (6000 × 2) : (8000 × 4) ⇒ Profit Ratio = 12000 : 12000 : 32000 ⇒ Dividing by 4000, we get the ratio as 3 : 3 : 8 ⇒ Sum of ratio parts = 3 + 3 + 8 = 14 parts ⇒ Value of 14 parts = 56000 ⇒ Value of 1 part = 56000 ÷ 14 = 4000 ⇒ Y's share = 3 parts = 3 × 4000 = 12000 ∴ The correct answer is Rs. 12,000. Related Concepts: Simple Partnership If all partners invest their capital for the same time period, the profit is shared exactly in the ratio of their invested capitals. Compound Partnership If the partners invest their capitals for different time periods, the profit is shared in the ratio of the product of capital and the time duration of their investment: P_(1) : P_(2) = C_(1)×T_(1) : C_(2)×T_(2). Working vs Sleeping Partner A working partner manages the business and usually receives a fixed salary or a certain percentage of the total profit, after which the remaining profit is distributed among all partners according to their investments.