Exam path · Partnership
Partnership questions give two or three people's capitals, sometimes for different periods, and a total profit, then ask for one person's share. When every partner invests for the same time, the profit splits in the ratio of the capitals. When the periods differ, it splits in the ratio of capital multiplied by time — capital-months — which is the one idea that answers nearly every version of this topic.
Partnership is a short, reliably scoreable arithmetic topic in banking and SSC quant, usually one question worth splitting a rupee amount rather than finding it. The only real skill is remembering that stake is capital times time, not capital alone — a candidate who applies the same-period shortcut to a different-period question gets a clean, wrong number instantly.
Try it against the clock. Partnership runs at 40s easy, 50s medium and 65s hard. The clock is stamped and judged on our server, so the limit you see is the deadline that is actually enforced — and it starts when you tap Start, not while the question is loading.
If every partner invests for the same length of time, profit splits directly in the ratio of the capitals — the time cancels out and can be ignored.
Capital-months is what each partner actually risks. A partner with a smaller capital held for longer can out-rank one with more capital held for less time, and only capital × time shows that correctly.
Find the ratio of the capital-month figures, cancel it to lowest terms, and add the parts. That sum is the denominator every partner's share divides by.
A partner holding 3 of 8 parts gets 3/8 of the profit, not 3/8 of the capital. Keep the profit and the capitals as two separate numbers until this last step.
| What the paper says | What it means |
|---|---|
| Both invest for the same period | Split follows the capitals alone — time cancels |
| Capitals equal, periods differ | Split follows the time alone — this time capital cancels |
| Both capital and time differ | Split follows capital × time — capital-months |
| A joins after B by k months | A's time is the total period minus k, not the full period |
Generated by the same engine that mints the ComputePrep daily. Each answer is computed from the numbers printed in the question, and the walkthrough below each one is the engine's own working — not a solution written afterwards. Reload this page's live drill and you get different numbers.
Imran invests ₹900 for 6 months.
Shalini invests ₹1000 for 9 months.
The profit is ₹1200.
What is Imran's share of the profit?
Karan invests ₹450 for 6 months.
Meera invests ₹600 for 9 months.
The profit is ₹1800.
What is Karan's share of the profit?
Deepak invests ₹3600 for 8 months.
Latha invests ₹4000 for 9 months.
The profit is ₹2250.
What is Deepak's share of the profit?
The wrong options are not random numbers. Each one is the result of a specific careless error for this topic, so picking one tells you which habit is costing you marks.
₹5,000 for 12 months and ₹4,000 for 6 months are not in the ratio 5:4. In capital-months they are 60,000:24,000 — 5:2 — and applying the same-period shortcut to this question gives a share that looks plausible and is wrong.
If a partner joins 3 months into a 12-month year, their stake is capital × 9, not capital × 12. Using the full year for every partner is the single commonest slip once a joining date appears in the question.
The ratio of capital-months tells you how to divide the profit. Applying that same ratio to divide up the total capital, or answering with a capital figure when the profit was asked for, is an easy trap under a clock.
The specific wrong numbers this topic produces, and what each one tells you about the step you took. If you have just got a question wrong and want to know which habit did it, start here.
₹800 is half the profit, which only holds if the capitals were equal. They are not: the ratio is 5,000:3,000, which reduces to 5:3. Eight parts share ₹1,600, so one part is ₹200, and A's five parts come to ₹1,000, not ₹800.
Because the periods are different, capital alone is not the stake. Capital-months are 6,000 × 8 = 48,000 for A and 4,000 × 6 = 24,000 for B — a 2:1 ratio, not 3:2. On a profit of ₹1,800, A's correct share is ₹1,200, not the ₹1,080 that splitting by capital alone gives.
Because an equal split assumes equal capital-months, which the question never said. With capital-months in the ratio 5:3:2 on a ₹3,000 profit, the ten parts are worth ₹300 each, so the shares are ₹1,500, ₹900 and ₹600 — not ₹1,000 each, which is what a headcount split produces.
Yes. Partnership is a standard arithmetic topic in the quantitative aptitude section of IBPS PO and Clerk, SBI PO and Clerk, and most SSC papers, usually appearing as a single question worth splitting a profit or loss between two or three investors.
When the time is the same for every partner, shares follow the ratio of the capitals. When the time differs, shares follow the ratio of capital multiplied by time — capital-months. There is no separate formula beyond forming that ratio and dividing the profit accordingly.
About 40 to 65 seconds in prelims, which is what this drill enforces on the server: 40 seconds on easy, 50 on medium and 65 on hard.
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