Math · Aptitude · Chapter 07

🤝 Partnership

Profit-sharing when partners invest different amounts for different times.

💡 Sharing Profit Fairly

When two or more people invest money in a business, they share the profit. But how much each gets depends on TWO things: how much they invested and how long they invested it.

The basic rule:

Profit ratio = Investment × Time (for each partner)

Simple partnership — all partners invest for the same time:

Ratio = ratio of investments. A invests ₹6,000, B invests ₹4,000 for same time → profit ratio = 6:4 = 3:2.

Compound partnership — investments are for different times:

Ratio = (capital × time) for each. A invests ₹6,000 for 8 months, B invests ₹4,000 for 12 months → ratio = (6000×8) : (4000×12) = 48000 : 48000 = 1:1.

⚡ Working vs sleeping partner

A working partner manages the business and gets extra (e.g. 10% of profit as salary). The rest is divided in capital ratio.

Example: Profit ₹10,000. Working partner gets 10% salary = ₹1,000. Remaining ₹9,000 split by investment ratio.

⚡ Joining mid-year

If a partner joins later, count only the months they were active.

A joins for full 12 months with ₹5000. B joins after 4 months with ₹3000 (so active 8 months). Ratio = (5000×12) : (3000×8) = 60000 : 24000 = 5:2.

⚡ Equivalent capital trick

Convert each partner's contribution to "1-month equivalent capital":
A = 5000 × 12 = 60,000 month-rupees
B = 3000 × 8 = 24,000 month-rupees
Then just divide profit in that ratio.

🎬

The Profit Split

Animation
A: ₹6000 × 12 MONTHS · B: ₹4000 × 12 MONTHS PARTNER A — capital × time = 72,000 72,000 PARTNER B — capital × time = 48,000 48,000 PROFIT ₹10,000 A ₹6000 B ₹4000 PROFIT-SHARING CALCULATION A's equivalent capital: 6000 × 12 = 72,000 B's equivalent capital: 4000 × 12 = 48,000 Ratio = 72,000 : 48,000 = 3 : 2 (simplified) A gets (3/5) × 10000 = ₹6,000 · B gets (2/5) × 10000 = ₹4,000

The capital-time bar of each partner determines their slice of the profit pie.

🧮

Partnership Calculator

Calculator
🤝 Two-partner profit split

A: ₹ × mo · B: ₹ × mo · Profit ₹

A gets ₹6,000 · B gets ₹4,000 · Ratio 3:2

Practice (SSC): A and B started a business with ₹15,000 and ₹20,000. After 6 months C joined them with ₹10,000. The annual profit was ₹30,000. Find each one's share.
A's capital-time: 15000 × 12 = 1,80,000. B: 20000 × 12 = 2,40,000. C: 10000 × 6 = 60,000.
Ratio: 180000 : 240000 : 60000 = 3 : 4 : 1. Total parts = 8.
A: (3/8) × 30000 = ₹11,250 · B: (4/8) × 30000 = ₹15,000 · C: (1/8) × 30000 = ₹3,750.
Practice (Banking): A invested ₹4,000 for 6 months in a business. B invested ₹6,000. If at the end of the year the profit ratio is 4:9, for how many months was B in the business?
A's equivalent: 4000 × 6 = 24000. Ratio 4:9. So B's equivalent = (24000 × 9)/4 = 54000. Time for B = 54000/6000 = 9 months.
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