
Shortcut Trick
Profit Ratio = (CapitalA × TimeA) : (CapitalB × TimeB)
Ratio = (75 × 12) : (80 × 7) = 900 : 560 = 45 : 28
Total Ratio = 45 + 28 = 73 units
73 units = ₹4,08,800 ⇒ 1 unit = ₹5,600
A’s share = 45 × 5,600 = ₹2,52,000
B’s share = 28 × 5,600 = ₹1,56,800
∴ The correct answer is ₹2,52,000 and ₹1,56,800.

Alternate Method
Given:
Investment of A = ₹75,000
Investment of B = ₹80,000
Time period of A = 12 months
Time period of B = 12 − 5 = 7 months
Total Profit = ₹4,08,800
Formula Used:
Profit Ratio = (Investment1 × Time1) : (Investment2 × Time2)
Partner A
₹75,000 × 12 m
Partner B
₹80,000 × 7 m
Ratio = 45 : 28
Calculations:
⇒ Profit share of A : Profit share of B = (75,000 × 12) : (80,000 × 7)
⇒ Ratio = 9,00,000 : 5,60,000
⇒ Ratio = 90 : 56 = 45 : 28
⇒ Total profit units = 45 + 28 = 73
⇒ Share of A = (45 ÷ 73) × 4,08,800
⇒ Share of A = 45 × 5,600 = ₹2,52,000
⇒ Share of B = (28 ÷ 73) × 4,08,800
⇒ Share of B = 28 × 5,600 = ₹1,56,800
∴ The correct answer is ₹2,52,000 and ₹1,56,800.

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 manages the business and may receive a salary before the remaining profit is shared according to the investment ratio.
Variable Investment
If investment changes during the period, use the sum of (Investment × Duration) for each interval: (C1t1 + C2t2 + ...).