Shortcut Trick
Initial capital ratio Amar : Bimal : Ravi = 105 : 40 : 36 (LCM of 2, 3, 5 is 30).
Effective capital ratio = (105 × 4 + 157.5 × 8) : (40 × 12) : (36 × 12) = 1680 : 480 : 432.
Simplified profit ratio = 35 : 10 : 9 (Total units = 54).
Bimal's share = (10 ÷ 54) × 54,21,600 = 10 × 1,00,400 = ₹10,04,000.
∴ The correct answer is ₹10,04,000.
Alternate Method
Given:
Initial investment ratio of Amar, Bimal, and Ravi = 7/2 : 4/3 : 6/5
Total profit after 1 year = ₹54,21,600
Formula Used:
Profit Share = Capital × Time
Calculations:
⇒ To simplify the ratio 7/2 : 4/3 : 6/5, multiply each term by the LCM of 2, 3, and 5 (which is 30).
⇒ Amar = 7/2 × 30 = 105; Bimal = 4/3 × 30 = 40; Ravi = 6/5 × 30 = 36.
⇒ Amar's total investment = (105 × 4) + (105 × 150/100 × 8)
⇒ Amar = 420 + (157.5 × 8) = 420 + 1260 = 1680.
⇒ Bimal's total investment = 40 × 12 = 480.
⇒ Ravi's total investment = 36 × 12 = 432.
⇒ Profit Ratio (A:B:R) = 1680 : 480 : 432.
⇒ Dividing by 48, we get 35 : 10 : 9.
⇒ Sum of ratios = 35 + 10 + 9 = 54 units.
⇒ 54 units = ₹54,21,600.
⇒ 1 unit = ₹54,21,600 ÷ 54 = ₹1,00,400.
⇒ Bimal's share = 10 units = 10 × 1,00,400 = ₹10,04,000.
∴ The correct answer is ₹10,04,000.
Additional Information
Partnership Profit Distribution
Profit is always distributed in the ratio of the product of Capital and Time (P = C × T).
Active vs Sleeping Partner
An active partner may receive a salary or a percentage of the profit for managing the business before the remaining profit is distributed among all partners.
Effective Capital
If a partner changes their investment amount during the period, effective capital is the sum of (amount × time) for each distinct period.