⏳ Capital × Time
2 exam question types, fully solvedReal 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.
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.
A: ₹40,000 for 12 months gives ; B: ₹20,000 for 6 months gives . So A : B = 4 : .
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 papersMoney left in longer earns more. Weight each partner by capital × time ("capital-months"), and subtract any joining delay from the total period first.
Key trap: if someone "joins after months", their money worked for months, not . 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 invests ₹60,000 for 12 months and B invests ₹45,000 for 8 months. Find the profit ratio A : B.
A starts a business with ₹24,000. B joins 6 months later with ₹36,000. Find the profit ratio A : B after 1 year.
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.
