Shortcut Trick
Assume C investment = x, then B = x + 10,000 and A = x + 17,000.
Total = 3x + 27,000 = 69,000 ⇒ x = 14,000.
Investment Ratio A : B : C = 31,000 : 24,000 : 14,000 = 31 : 24 : 14.
Total Ratio parts = 31 + 24 + 14 = 69.
A share = (31 / 69) × 32,154 = 31 × 466 = 14,446.
∴ The correct answer is ₹14,446.
Alternate Method
Given:
Total Investment of A, B and C = ₹69,000
Total Profit = ₹32,154
Investment conditions: A = B + ₹7,000; B = C + ₹10,000
Formula Used:
Profit Share ∝ Investment × Time
Since time is the same for all, Profit Ratio = Investment Ratio.
Calculations:
⇒ Let C investment = ₹x
⇒ B investment = ₹(x + 10,000)
⇒ A investment = ₹(x + 10,000 + 7,000) = ₹(x + 17,000)
⇒ x + (x + 10,000) + (x + 17,000) = 69,000
⇒ 3x + 27,000 = 69,000
⇒ 3x = 42,000 ⇒ x = 14,000
⇒ A investment = 14,000 + 17,000 = 31,000
⇒ B investment = 14,000 + 10,000 = 24,000
⇒ Ratio A : B : C = 31,000 : 24,000 : 14,000 = 31 : 24 : 14
⇒ Total ratio units = 31 + 24 + 14 = 69
⇒ 69 units = 32,154
⇒ 1 unit = 32,154 ÷ 69 = 466
⇒ share of A = 31 × 466 = 14,446
∴ The correct answer is ₹14,446.
Additional Information
Simple Partnership
When all partners invest their capital for the same duration of time, the profit is divided in the ratio of their investments (P1 : P2 = C1 : C2).
Compound Partnership
When partners invest for different time periods, the profit is shared in the ratio of the product of their capital and time (Profit = Capital × Time).
Working vs Sleeping Partner
A working partner manages the business and may receive a salary, while a sleeping partner only provides capital and shares profits accordingly.