Shortcut Trick
Profit ratio of A : B = (Capital × Time) ratio
A : B = (20,000 × 2) : (30,000 × 3) = 40,000 : 90,000 = 4 : 9
A's share = 4 units = ₹4,000
B's share = 9 units = (4,000 ÷ 4) × 9 = ₹9,000
∴ The correct answer is ₹9,000.
Alternate Method
Given:
Investment of A = ₹20,000, Time = 2 years
Investment of B = ₹30,000, Time = 3 years
Profit share of A = ₹4,000
Formula Used:
Profit Ratio = (Capital1 × Time1) : (Capital2 × Time2)
Calculations:
⇒ Effective capital of A = 20,000 × 2 = ₹40,000
⇒ Effective capital of B = 30,000 × 3 = ₹90,000
⇒ Ratio of profits (A : B) = 40,000 : 90,000 = 4 : 9
⇒ Let the common ratio factor be x.
⇒ A's share = 4x = 4,000
⇒ x = 4,000 ÷ 4 = 1,000
⇒ B's share = 9x = 9 × 1,000
⇒ B's share = ₹9,000
∴ The correct answer is ₹9,000.
Additional Information
Basic Partnership Rule
Profit is always distributed in the ratio of the product of the capital invested and the time for which it is invested: Profit Ratio = C1T1 : C2T2.
Compound Partnership
When partners invest different amounts for different periods of time, it is called a compound partnership, requiring the use of weighted capital over time.
Types of Partners
An Active Partner manages the business and may take a salary before profit distribution, whereas a Sleeping Partner only invests money.