Partnership

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Partnership — Key Facts for SSC CGL • When two or more persons invest money together to run a business, they form a partnership. The money invested is called capital, and the agreement about profit-sharing is called the partnership deed. • Simple Partnership: All capital is invested for the same period. Profit ratio = Capital ratio. • Compound Partnership: Capital is invested for different periods. Profit ratio = Capital × Time. • The share of profit is calculated as: $\text{Profit Share} = \dfrac{\text{Capital of Partner} \times \text{Time}}{\text{Total Capital} \times \text{Total Time}}$ • Working Partner: A partner who actively manages the business may receive a salary or commission, separate from profit share. • If partners invest for different durations: $\text{Profit Ratio} = P_1 \times T_1 : P_2 \times T_2$

⚡ Exam Tip: SSC CGL frequently asks questions where partners join or leave at different times. Always convert time to the same unit (months/years) before calculating the ratio. A common trap is forgetting that a partner who joins mid-year still deserves profit for the period they were active.

---

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Partnership — SSC CGL Study Guide

Core Concept: A partnership is formed when two or more individuals combine capital to conduct business and share profits according to a pre-agreed ratio. The fundamental principle is that profit-sharing is directly proportional to the amount of capital invested and the duration for which it remains invested.

Key Formula — Profit Sharing in Compound Partnership: If Partner A invests ₹$P_A$ for $T_A$ months and Partner B invests ₹$P_B$ for $T_B$ months, then:

$$\frac{\text{Profit of A}}{\text{Profit of B}} = \frac{P_A \times T_A}{P_B \times T_B}$$

Worked Example 1 (Simple Partnership): Rahul invests ₹40,000 and Ramesh invests ₹60,000 in a business. They share profits in the ratio of their capitals. If the total profit after one year is ₹25,000, find Rahul’s share.

• Capital Ratio = 40,000 : 60,000 = 2 : 3
• Rahul’s Share = $\frac{2}{5} \times 25{,}000 = ₹10{,}000$

Worked Example 2 (Compound Partnership): Amit invests ₹30,000 for 8 months and Binoy invests ₹50,000 for 6 months. If the total profit is ₹13,500, find each person’s share.

• Amit’s contribution = $30{,}000 \times 8 = 2{,}40{,}000$
• Binoy’s contribution = $50{,}000 \times 6 = 3{,}00{,}000$
• Ratio = $2{,}40{,}000 : 3{,}00{,}000 = 4 : 5$
• Total parts = 9; Amit’s profit = $\frac{4}{9} \times 13{,}500 = ₹6{,}000$; Binoy = ₹7,500

Common Student Mistakes: Converting time units incorrectly (mixing months and years), forgetting to square the capital when dealing with compound ratios, and incorrectly adding salary/commission before calculating the profit-sharing ratio.

---

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Partnership — Comprehensive SSC CGL Notes

Theoretical Foundation: Partnership is a fundamental concept in commercial mathematics tested extensively in SSC CGL Tier-I (Quantitative Aptitude) and Tier-II (Mathematics). The principle is rooted in the idea that capital and time are both limited resources — a partner who leaves early but invested heavily may still earn more than a partner who stayed longer but invested less. The core formula for compound partnership was first formalised in Indian commercial mathematics education and remains unchanged across decades of exam patterns.

Advanced Variants Tested in SSC CGL:

1. Partner Joining Mid-Period: When a new partner joins after some time, the profit-sharing ratio changes. Calculate old partners’ shares for the period before the new partner joined, then recalculate for the combined period.

2. Partner Retiring Mid-Period: A retiring partner is entitled to profit only for the period of their active involvement.

3. Salary/Commission in Partnership: If a working partner receives a salary, deduct this from the total profit before distributing the remainder in the capital ratio.

Example — Partner Joining: Sameer invests ₹20,000 for 6 months. After 6 months, Raj joins with ₹30,000. Total profit after 1 year = ₹41,000. Find each share.

• Sameer’s contribution = $20{,}000 \times 6 = 1{,}20{,}000$
• Raj’s contribution = $30{,}000 \times 6 = 1{,}80{,}000$
• Ratio = $1{,}20{,}000 : 1{,}80{,}000 = 2 : 3$
• Sameer = $\frac{2}{5} \times 41{,}000 = ₹16{,}400$; Raj = ₹24,600

Example — With Working Partner Commission: Two partners A and B invest ₹40,000 and ₹60,000 respectively. A is a working partner and receives 10% of the total profit as commission. Total profit = ₹30,000. Find each share.

• Commission to A = 10% of 30,000 = ₹3,000
• Remaining profit = ₹27,000 (to be split in capital ratio 2:3)
• A’s share = $₹3{,}000 + \frac{2}{5} \times 27{,}000 = ₹3{,}000 + ₹10{,}800 = ₹13{,}800$
• B’s share = $\frac{3}{5} \times 27{,}000 = ₹16{,}200$

SSC CGL PYQ Pattern: Partnership questions appear in Tier-I (2020-2023: 1-2 questions per exam) and Tier-II (2019-2023: consistently 2-3 questions per exam). Most questions are of moderate difficulty and can be solved in 60-90 seconds with the formula approach.

Practice Strategy: Focus on compound partnership problems where partners invest for different durations, and problems where partners join at staggered intervals. These variants are most frequently combined with ratio-proportion concepts in Tier-II.

---

Content adapted based on your selected roadmap duration. Switch tiers using the pill selector above.