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Partnership

ITBP Constable · Quantitative Aptitude

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Core Concept

Read this first — the foundation of the topic

→Simple Partnership

All partners invest for the same time period 2

→Compound Partnership

Partners invest for different time periods Core

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Formula Block

Memorise — at least one formula appears in every paper

For Simple Partnership: Profit Ratio = Investment Ratio

For Compound Partnership: Profit Ratio = (Investment × Time) Ratio

If A invests Rs. X for T1 months and B invests Rs. Y for T2 months:

Profit sharing ratio = (X × T1) : (Y × T2)

Key Rules:

- Partners share profit in the ratio of their investments

- Time factor only matters when investment periods are different

- Total profit is distributed among all partners

- Working partners may get additional salary before profit distribution

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Exam Patterns

What examiners ask — read before attempting PYQs

✏️Worked Example 1

1

Calculate effective investments A: 20,000 × 12 = 2,40,000 B: 30,000 × 8 = 2,40,000 C: 40,000 × 6 = 2,40,000

2

Find ratio Ratio = 2,40,000 : 2,40,000 : 2,40,000 = 1:1:1

3

Calculate A's share A's share = (1/3) × 61,800 = Rs. 20,600 Worked Example 2: P and Q enter into partnership. P invests Rs. 40,000 and Q invests Rs. 60,000. After 6 months, P withdraws Rs. 10,000. If the profit at year-end is Rs. 33,000, find Q's share.

1

Calculate P's effective investment First 6 months: 40,000 × 6 = 2,40,000 Next 6 months: 30,000 × 6 = 1,80,000 P's total = 4,20,000

2

Calculate Q's effective investment Q invests for full year: 60,000 × 12 = 7,20,000

3

Find ratio P : Q = 4,20,000 : 7,20,000 = 7:12

4

Calculate Q's share Q's share = (12/19) × 33,000 = Rs. 20,842 (approximately) Shortcut Trick #3 - The Percentage Method: If working with percentages, convert everything to the same base (usually 100) before calculating ratios

⚠️Common Mistake Alert

The #1 mistake students make is forgetting to account for time differences in compound partnerships. Many students only consider the investment amounts and ignore the time factor completely. Always check if all partners invested for the same duration before applying simple partnership formulas. When time periods differ, you MUST multiply investment by time to get the effective investment ratio.

🔑 Key Points

Partnership profit sharing is always based on investment ratios when time periods are equal
For different time periods, multiply investment amount by time duration to get effective investment
Simple Partnership formula: Profit Ratio = Investment Ratio
Compound Partnership formula: Profit Ratio = (Investment × Time) Ratio
Quick ratio trick: If investments are in ratio a:b, profits will also be in ratio a:b for equal time
Working partners may receive salary first before profit distribution among all partners
Time factor formula: Effective Investment = Amount × Number of months invested
Unity method: Find one unit value by dividing known profit by its ratio share
Always convert time periods to same unit (months or years) before calculation
Total profit equals sum of all individual partner shares in the given ratio

📌 Exam Facts

Partnership problems appear in 1-2 questions every year in SSC CGL Tier-I
Investment ratio 2:3:4 means partners get profits in exactly same ratio 2:3:4
If A invests for 12 months and B for 6 months with equal amounts, A gets double profit share
Working partner salary is deducted from total profit before distribution
Compound partnership formula: (A × T1) : (B × T2) where A,B are investments and T1,T2 are time periods
Simple partnership applies only when all investment periods are identical
Partnership profit sharing follows the same rules as direct proportion in mathematics

🚀 60-Second Revision

Remember: Multiply investment by time period for compound partnerships
Formula: Profit Ratio = (Investment × Time) Ratio for different time periods
Trap: Never ignore time differences - always check if periods are equal
Quick check: Total of individual shares should equal total profit given
Shortcut: Use unity method when one partner's actual profit is known
Pattern: Investment ratio and profit ratio are always identical in simple partnerships

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