Shortcut Trick
Initial investment ratio of X and Y is 3 : 2 ⇒ 30,000 : 20,000.
Equivalent investment of X = (30,000 × 6) + (15,000 × 6) = 2,70,000.
Equivalent investment of Y = (20,000 × 6) + (30,000 × 6) = 3,00,000.
Profit Ratio (X : Y) = 27 : 30 = 9 : 10.
Difference in share = (10 − 9) / (10 + 9) × 38,000 = 1/19 × 38,000 = ₹2,000.
∴ The correct answer is Y’s share is greater by ₹2,000.
Alternate Method
Given: Initial investment ratio X : Y = 3 : 2. Initial capital of X = ₹30,000. Total Profit = ₹38,000.
Formula Used: Profit Share Ratio = (Investment1 × Time1) : (Investment2 × Time2)
⇒ If 3 units = ₹30,000, then 1 unit = ₹10,000.
⇒ Y’s initial investment = 2 units = 2 × 10,000 = ₹20,000.
⇒ X’s total weightage = (30,000 × 6) + (15,000 × 6) = 1,80,000 + 90,000 = ₹2,70,000.
⇒ Y’s total weightage = (20,000 × 6) + (30,000 × 6) = 1,20,000 + 1,80,000 = ₹3,00,000.
⇒ Profit Ratio (X : Y) = 2,70,000 : 3,00,000 = 27 : 30 = 9 : 10.
⇒ Total ratio units = 9 + 10 = 19 units.
⇒ 19 units = ₹38,000 ⇒ 1 unit = ₹2,000.
⇒ Difference in shares = 10 units − 9 units = 1 unit.
⇒ Difference amount = 1 × 2,000 = ₹2,000.
∴ The correct answer is Y’s share is greater by ₹2,000.
Additional Information
Compound Partnership
When partners invest different capitals for different periods of time, the profit is distributed in the ratio of their monthly equivalent investment (Capital × Time).
Ratio of Profits
If partners P1 and P2 invest C1 and C2 for times T1 and T2, then Profit1 : Profit2 = C1T1 : C2T2.
Active vs. Sleeping Partner
An active partner manages the business and may receive a fixed salary or commission from the total profit before the remaining profit is shared according to investment ratios.