Shortcut Trick
Profit Ratio = P : Q : R = 14000 : 18000 : 24000 = 7 : 9 : 12
Difference in ratio parts of P and Q = 9 − 7 = 2 parts
Total ratio parts = 7 + 9 + 12 = 28 parts
Difference in profit share = (2 / 28) × 25480 = 25480 / 14 = 1820
∴ The correct answer is Rs. 1820.
Alternate Method
Given:
Investment of P = Rs. 14000
Investment of Q = Rs. 18000
Investment of R = Rs. 24000
Total Profit = Rs. 25480
Time period for all = 1 year
Formula Used:
Profit Ratio = (Capital of A × Time of A) : (Capital of B × Time of B) : (Capital of C × Time of C)
Calculation:
⇒ Profit Ratio of P, Q, and R = (14000 × 1) : (18000 × 1) : (24000 × 1)
⇒ Profit Ratio = 14 : 18 : 24
⇒ Simplified Ratio = 7 : 9 : 12
⇒ Sum of profit ratios = 7 + 9 + 12 = 28
⇒ Difference in profit ratio of P and Q = 9 − 7 = 2
⇒ Difference in profit share = (2 / 28) × 25480
⇒ Difference = (1 / 14) × 25480
⇒ Difference = 1820
∴ The correct answer is Rs. 1820.
Additional Information
Simple vs Compound Partnership
In a simple partnership, capitals are invested for the same time period. Profit is divided solely in the ratio of the invested capitals. In a compound partnership, the time periods differ, so the profit ratio becomes C1T1 : C2T2.
Active and Sleeping Partners
An active partner manages the business and usually receives a fixed salary or a specific percentage of the total profit for management duties. The remaining profit is then distributed according to the capital investment ratios among all partners including sleeping partners.
Finding Capital or Time from Profit
If the profit ratio and time ratio are given, Capital Ratio = (P1 / T1) : (P2 / T2). Conversely, if the profit and capital ratios are given, Time Ratio = (P1 / C1) : (P2 / C2).