Shortcut Trick
Investment Ratio A : B : C = (12 × 12) : (18 × 12) : (24 × 6)
Simplifying the ratio: 144 : 216 : 144 ⇒ 2 : 3 : 2
Total ratio parts = 2 + 3 + 2 = 7 units
Total profit ₹ 54,000 ⇒ 1 unit = 54,000 ÷ 7
C’s share (2 units) = (2 ÷ 7) × 54,000 = ₹ 15,428.57
∴ The correct answer is ₹ 15,428.57.
Alternate Method
Given:
Investment of A = ₹ 12,000 for 12 months
Investment of B = ₹ 18,000 for 12 months
Investment of C = ₹ 24,000 for (12 − 6) = 6 months
Total Profit = ₹ 54,000
Formula Used:
Profit Ratio = (Capital1 × Time1) : (Capital2 × Time2) : (Capital3 × Time3)
Calculations:
⇒ Ratio of Profit = (12,000 × 12) : (18,000 × 12) : (24,000 × 6)
⇒ Ratio of Profit = 144,000 : 216,000 : 144,000
⇒ Ratio of Profit = 144 : 216 : 144
⇒ Dividing by 72: 2 : 3 : 2
⇒ Total Share = 2 + 3 + 2 = 7 units
⇒ 7 units = ₹ 54,000
⇒ 1 unit = 54,000 ÷ 7
⇒ C’s share = 2 units = (2 × 54,000) ÷ 7
⇒ C’s share = 108,000 ÷ 7
⇒ C’s share = ₹ 15,428.5714...
∴ The correct answer is ₹ 15,428.57.
Additional Information
Partnership Profit Rule
When investments are for different time periods, the profit is distributed in the ratio of the product of Capital and Time (C1T1 : C2T2).
Working vs. Sleeping Partner
A working partner manages the business and may receive a salary or fixed percentage of profit before the remaining profit is divided according to the investment ratio.
Ratio Division
To find an individual's share from a total T with ratio a:b:c, use the formula: Share of A = [a ÷ (a+b+c)] × T.