Shortcut Trick
Ratio of Profit Share = (Capital × Time)
A : B : C = (60 × 10) : (75 × 8) : (90 × x) = 600 : 600 : 90x = 20 : 20 : 3x
A's share = 20 ÷ (20 + 20 + 3x) = 1/4
80 = 40 + 3x ⇒ 3x = 40 ⇒ x = 40/3 = 131/3
∴ The correct answer is 13(1)/(3) months.
Alternate Method
Given:
Investment of A = ₹60,000 for 10 months
Investment of B = ₹75,000 for 8 months
Investment of C = ₹90,000 for x months
A's Profit = 1/4 of Total Profit
Formula Used:
Profit Share = Capital × Time period
Calculations:
⇒ Total Profit-equivalent for A = 60,000 × 10 = 6,00,000
⇒ Total Profit-equivalent for B = 75,000 × 8 = 6,00,000
⇒ Total Profit-equivalent for C = 90,000 × x = 90,000x
⇒ Total Profit in units = 6,00,000 + 6,00,000 + 90,000x = 12,00,000 + 90,000x
⇒ According to the question, A's share = 1/4 × Total Profit
⇒ 6,00,000 = (1/4) × (12,00,000 + 90,000x)
⇒ 6,00,000 × 4 = 12,00,000 + 90,000x
⇒ 24,00,000 = 12,00,000 + 90,000x
⇒ 90,000x = 12,00,000
⇒ x = 12,00,000 ÷ 90,000
⇒ x = 120 ÷ 9 = 40 ÷ 3 = 131/3 months
∴ The correct answer is 13(1)/(3) months.
Additional Information
Partnership Profit Sharing Rule
Profit is always distributed in the ratio of the product of Capital and Time: P1 : P2 = (C1 × T1) : (C2 × T2).
Active vs Sleeping Partner
An Active partner manages the business and may receive a salary/commission before the remaining profit is divided, while a Sleeping partner only invests money.
Total Profit Calculation
If A's share is 1/n, then (Total Profit) = n × (A's Profit), which means the sum of all partners' capital-time products equals n times A's product.