Partnership Business

“Partnership questions are based on capital investment and time. Frequently asked in SSC, Railway, Banking, and Defence exams.”

1. Basic Concepts and Formulas

If two persons A and B invest capital in the ratio A:B, then profit is also shared in the ratio A:B.
If time is involved: Profit ∝ Capital × Time
Total profit is divided in ratio of (Capital × Time)
If a partner joins late or withdraws early, only active time is considered for profit calculation.

Type 1: Simple Investment Ratio
Example: A:B = 3:2 ⇒ Profit = 3:2
Type 2: Capital × Time Ratio
Example: A = ₹5000 for 12 months, B = ₹6000 for 10 months
⇒ Ratio = (5000×12):(6000×10) = 60:60 = 1:1
Type 3: New Partner Joins Later
Example: A invests ₹8000 for 12 months, B joins after 4 months with ₹12000
⇒ A = 8000×12 = 96000, B = 12000×8 = 96000 ⇒ Profit = 1:1
Type 4: Total Profit Distribution
Example: Total profit = ₹24000, A:B = 2:1 ⇒ A = ₹16000, B = ₹8000
Type 5: Find Capital or Time
Example: Profit ratio = 3:2, A invested ₹6000 for 12 months ⇒ B = (6000×12×2)/3 = ₹48000 for 1 month (or solve for time)

(SSC CGL 2022): A invests ₹6000 for 12 months, B ₹8000 for 6 months. Find profit ratio?
Solution: A = 6000×12 = 72000, B = 8000×6 = 48000 ⇒ Ratio = 3:2
(RRB NTPC 2020): A and B share profits in 5:3. If A invests ₹25000 for 12 months, for how long did B invest ₹20000?
Solution: (25000×12):(20000×t) = 5:3 ⇒ t = 7.5 months
(SSC CHSL 2019): A starts a business, B joins after 4 months. Capital ratio = 3:2. If total profit is ₹8400, find B’s share.
Solution: A = 3×12 = 36, B = 2×8 = 16 ⇒ Total = 52 ⇒ B’s share = (16/52)×8400 = ₹2584.62
(HSSC 2021): A:B = 4:5, B:C = 2:3 ⇒ A:B:C = 8:10:15. If profit is ₹6600, find A’s share = (8/33)×6600 = ₹1600