Partnership

Partnership questions combine ratio and time into a single, very scoreable pattern, and SBI Clerk usually offers one each shift as an easy mark. Two or more people invest capital for some period and share the profit in proportion to their contribution. The one rule that unlocks the entire topic is that a partner's share of profit is proportional to capital multiplied by time. Once you compute each partner's capital-times-time, the profit split is an ordinary dividing-a-sum-in-a-ratio question you already know.

Profit Sharing by Capital times Time

Work out capital × time for every partner, reduce the resulting numbers to a simple ratio, and split the profit in that ratio. If A puts in 5,000 for 12 months and B puts in 6,000 for 8 months, their ratio is (5000×12) : (6000×8) = 60,000 : 48,000 = 5 : 4. When all partners invest for the same duration, time cancels out and the profit simply follows the capital ratio, which is the quickest sub-case and worth spotting immediately to save the multiplication.

Profit share ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂) : …

When Capital or Time Changes Midway

Some questions have a partner add or withdraw money partway through the year, so split that partner's contribution into periods and add the capital × time of each period. A partner with 8,000 for 5 months and then 10,000 for the remaining 7 months contributes 8000×5 + 10000×7 = 40,000 + 70,000 = 1,10,000 in capital-months. Treat each period as if it were a separate small investment and sum them; the combined figure then enters the profit ratio exactly like any fixed contribution.

Active and Sleeping Partners

A working or active partner runs the business and often takes a salary or a commission before profits are divided, while a sleeping partner only invests money and shares the balance. In such questions, first remove the active partner's salary or commission from the total profit, then divide whatever remains in the capital-times-time ratio. Reading whether a stated amount is a salary taken off the top or a share of the remaining profit is the key decision, because applying it at the wrong stage changes every partner's final figure.

Solved Examples

Example 1: A invests 12,000 for 6 months, B invests 9,000 for 8 months. Ratio = 72,000 : 72,000 = 1 : 1, so a profit of 8,400 splits as 4,200 each.

Example 2: P and Q invest 20,000 and 30,000 for the same year. Time cancels, so profit of 15,000 splits as 2 : 3, giving P 6,000 and Q 9,000.

✗ Splitting profit by capital alone when the times differ  |  ✓ Using capital × time for each partner before forming the ratio