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Partnership · Topic 2 of 5

⏳ Capital × Time

2 exam question types, fully solved

Real partners rarely invest for the same time — one joins late, another pulls money out early. A smaller amount left in for longer can earn more than a big amount left in briefly. So we weigh each partner by capital × time.

Reduce everyone to “capital-months”

Profit share is proportional to capital multiplied by the number of months it stayed in:

• Joined late? If someone joins months after the start, their money worked for months, not . Always subtract the delay from the total period.

• Don't multiply blindly. Simplify the capital ratio and the time ratio separately, then multiply across. For for 12 mo vs for 8 mo: capitals , times , so ratio .

• Capital changed mid-year? Treat each stretch on its own and add the capital-months: . After a withdrawal, use what is left, not what was taken out.

🤝Profit SplitterEnter capital & time for each partner
A120.0K
B120.0K
C—
ProfitSplit
Partner A50.0%
Partner B50.0%
Ratio : A: 1 : B: 1

A: ₹40,000 for 12 months gives ; B: ₹20,000 for 6 months gives . So A : B = 4 : .

📝Practice Questions

Q1A invests ₹50,000 for 12 months and B invests ₹50,000 for 6 months. The profit ratio A : B is:

Q2P starts with ₹30,000. Q joins 8 months later with ₹60,000. The profit ratio P : Q is:

Q3A invests ₹40,000 for 12 months and B invests ₹60,000 for 6 months. The profit ratio A : B is:

📚

Real exam questions — Capital × Time

2 question types · 7 solved examples from real SSC papers

Money left in longer earns more. Weight each partner by capital × time ("capital-months"), and subtract any joining delay from the total period first.

How to solve this type
Money that stays longer earns more, so each partner's weight is capital × time (think "capital-months"). Build the ratio (C1T1):(C2T2):…(C_1 T_1) : (C_2 T_2) : \dots, cancel the common zeros and a common factor, then split the profit by that ratio.
Key trap: if someone "joins after nn months", their money worked for (12−n)(12 - n) months, not nn. Subtract the delay from the total period first.

Ramesh starts a business investing ₹40,000. Six months later Kevin joins with ₹20,000. The profit at year end is ₹10,000. Kevin's share is:

A₹3,000B₹2,500C₹2,000D₹4,000

A invests ₹60,000 for 12 months and B invests ₹45,000 for 8 months. Find the profit ratio A : B.

A2 : 1B5 : 3C4 : 3D3 : 2

A starts a business with ₹24,000. B joins 6 months later with ₹36,000. Find the profit ratio A : B after 1 year.

A5 : 3B4 : 3C3 : 2D2 : 1

A invests ₹48,000 for the full year, B invests ₹36,000 for 8 months and C invests ₹24,000 for 6 months. Find the profit ratio A : B : C.

A6 : 4 : 2B4 : 3 : 2C8 : 6 : 3D8 : 4 : 2