Partnership, at its core, is a weighted-ratio problem. Two or more people pool money, and at the end of a period, they split profits in proportion to what each person actually contributed — not just the amount invested, but the amount multiplied by the time for which it was invested.
Think of it this way: if you park ₹1,00,000 in a business for 12 months and your friend parks ₹2,00,000 for only 3 months, who contributed more? The raw numbers say your friend, but the weighted reality says you did — ₹12,00,000 of capital-months versus ₹6,00,000. That ratio, 2:1, becomes the profit-sharing ratio.
This is the entire engine of partnership problems:
Profit share ∝ Capital × Time
Everything else — sleeping partners, different joining dates, changed investments mid-period — is just a variation of this one idea.
Two types of partners you will encounter:
The analogy that works: imagine profit as a shared pizza. Each person's slice is proportional to how much dough (capital) they kneaded and for how long (time). If someone joined late, they kneaded for fewer hours — smaller slice, regardless of how much dough they brought.
SSC CGL tests this topic almost every year. The questions are clean — no tricks hidden in the language, only in the arithmetic. Speed comes from computing capital-months quickly and reducing ratios before multiplying into the total profit.
For each partner, compute:
The profit-sharing ratio is:
Once you have the ratio, a partner's share is:
This is where most errors happen. If a business runs for N months total and a partner joins k months late, that partner's time is N - k months, not N.
Look — always draw a timeline for problems with three or more partners. Mark when each person joined and calculate individual time periods carefully before multiplying by capital.
Example walkthrough: A starts in January. B joins in May (4 months later). C joins in September (8 months later). Business ends in December.
Now multiply each by their capital to get the ratio.
Some problems give you a partner who invests an amount for part of the year and a different amount for the rest. Here, split that partner's contribution into two segments and add them.
If Partner Y invests ₹P for t₁ months, then changes to ₹Q for t₂ months:
This is precisely what the second PYQ in this set tests — do not try to average the amounts, calculate each segment separately.
A critical speed habit: reduce the capital-months ratio before computing profit shares. Dividing out common factors early saves you from multiplying large numbers and then simplifying.
Here's the trick — after computing all capital-months figures, find the GCD of all values and divide through. You work with smaller numbers for the final fraction calculation.
Example: Capital-months are 9,60,000 : 9,60,000 : 6,40,000.
Divide everything by 3,20,000 → ratio becomes 3 : 3 : 2. Now the arithmetic is trivial.
If a working partner takes x% of profit as salary first:
Salary = x% of Total ProfitTotal Profit - SalarySSC CGL rarely makes this multi-step, but if the question says "A gets 10% of profit for managing the business before profit is divided," that is the structure to apply.
Occasionally, the question gives interest rates instead of absolute capitals. Treat Capital × Rate as the effective contribution (time is uniform, so it cancels). The ratio becomes:
This is just the capital-months idea with rate replacing time.
Before any calculation, write a two-column table: | Partner | Capital × Time |. Fill it in, then divide by GCD. This structured habit prevents the most common error — computing ratios from raw capital figures without accounting for time.
Standard unstructured approach: 60-90 seconds of mental juggling with risk of error. Structured table: 30-40 seconds, near-zero error rate. The table forces you to separate "what they invested" from "how long they invested it," which is exactly the distinction these questions test.
When two partners' capital × time values are equal, their profit ratio is 1:1 — regardless of how different the raw numbers look. Recognize this pattern instantly.
Example: A invests ₹80,000 for 9 months = 72,00,000. B invests ₹1,20,000 for 6 months = 72,00,000. Ratio = 1:1. Standard approach: compute both products, simplify. Shortcut recognition: as soon as you see two products are equal, write 1:1 and move to the profit split. Saves 2-3 computational steps. The fourth PYQ in this set is exactly this trap.
Before computing capital × time, cancel zeros from the capital figures. If all capitals are multiples of ₹10,000, divide each by 10,000 first, then multiply by time.
Example: ₹80,000 for 12 months, ₹1,20,000 for 8 months, ₹1,60,000 for 4 months. Scale down: 8, 12, 16. Now: 8×12=96, 12×8=96, 16×4=64. Ratio = 96:96:64 = 3:3:2. You worked with single/double digit numbers throughout instead of hundreds of thousands. Cuts arithmetic time by 40-50% and reduces transcription errors.
Instead of computing the full ratio first and then dividing total profit, identify a partner's fraction directly.
If the ratio is A:B:C = 3:3:2, total parts = 8. C's fraction = 2/8 = 1/4. Apply directly: C's share = (1/4) × Total Profit. No need to separately find A's and B's shares unless asked. For a "find one partner's share" question, this shaves off one unnecessary computation. Standard: compute all three shares, identify C's. Shortcut: compute only C's fraction × profit. Saves 1 multiplication and 1 subtraction.
When a partner joins k months after the business starts, and the total period is N months, their time is always N - k. Write this as a subtraction the moment you read the problem.
For Jatin in the first PYQ: total period = 24 months, delay = 8 months, so time = 24 - 8 = 16 months. Done in one line. The error trap is using 8 (the delay) as the time, or using 24 - 8 = 16 but then second-guessing whether to add or subtract. Commit to N - k every single time. Eliminates a common 30-second re-reading loop.
When you see a partnership question in the exam hall, run through this decision path:
Step 1 — Count partners and identify joining dates. Write down each partner's capital and the month they joined.
Step 2 — Compute each partner's time period. Time = Total period - Months before joining. If investment changes mid-period, split into two rows.
Step 3 — Scale down capitals. Cancel common zeros (divide by ₹10,000 or ₹1,000 as appropriate).
Step 4 — Multiply scaled capital by time. Write capital-months for each partner.
Step 5 — Find GCD and simplify ratio. Work with the simplified ratio going forward.
Step 6 — Check if question asks for ratio or actual rupee amount. If ratio, stop here. If rupee amount, compute (partner's ratio part / total parts) × total profit.
Time budget: Simple two-partner problems — under 60 seconds. Three-partner with different joining dates — 90 seconds. If you cross 2 minutes on any partnership problem, something is wrong with your Step 2 or Step 5. Stop, re-check the timeline.
Why this question: The classic "one partner joins late" structure. Tests whether you use the full 24-month period for the late joiner or correctly subtract the delay.
Solving path: Total period = 2 years = 24 months. Gautam invested from month 1, so his time = 24 months. Jatin joined 8 months later, so his time = 24 - 8 = 16 months. Scale down capitals: 60 → 6, 35 → 3.5 (or keep as 60 and 35). Capital-months: Gautam = 60 × 24 = 1440, Jatin = 35 × 16 = 560. Ratio = 1440 : 560. Divide by 80 → 18 : 7. Answer: 18 : 7.
Why this question: A more complex variant where each partner's investment changes at different points — you must split each contribution into segments.
Solving path: The question implies specific investment amounts at different rates/times. Following the explanation's arithmetic: X's capital-months = 2 × 18 = 36. Y's = 3 × 6 + 1.5 × 12 = 18 + 18 = 36. Z's = 5 × 3 + 3 × 15 = 15 + 45 = 60. Ratio = 36 : 36 : 60. Divide by 12 → 3 : 3 : 5. Answer: 3 : 3 : 5.
Why this question: Three partners with staggered joining times. Tests your ability to correctly identify each partner's active months within a 12-month window.
Solving path: Arvind joins at start (month 0) → 12 months active. Bhavin joins at month 4 → 12 - 4 = 8 months active. Chandan joins at month 8 → 12 - 8 = 4 months active. Scale down capitals by ÷ 10,000: 8, 12, 16. Capital-months: 8 × 12 = 96, 12 × 8 = 96, 16 × 4 = 64. Total = 256. Chandan's fraction = 64/256 = 1/4. Share = (1/4) × 1,05,000 = ₹26,250. Answer: ₹26,250.
Why this question: The equal capital-months trap. Raw capitals and times look very different, but the products are equal — leading to a 1:1 ratio that many students miss.
Solving path: Scale down capitals by ÷ 10,000: A = 8, B = 12. A's capital-months = 8 × 9 = 72. B's capital-months = 12 × 6 = 72. Ratio = 72 : 72 = 1 : 1. B's share = (1/2) × 45,000 = ₹22,500. Answer: ₹22,500. Note: many students see ₹1,20,000 > ₹80,000 and assume B gets more — the time difference cancels this completely.
Using delay period as the time period. If Jatin joins 8 months late in a 2-year business, his time is 16 months — not 8. The delay is not the working period. Always compute: Total period minus delay.
Forgetting to convert years to months when mixing units. "Two years" = 24 months. If one partner's time is given in months and another in years, convert everything to the same unit before multiplying. A ratio built on mixed units is wrong.
Taking the raw capital ratio as the profit ratio. This only holds when all partners invest for exactly the same duration. The moment joining dates differ, raw capital ratio is meaningless — you must multiply by time.
Not splitting mid-period investment changes. If a partner increases or decreases their investment after a few months, calculate two separate capital-months values and add them. Averaging the investment amounts is incorrect and will always give a different (wrong) answer.
Computing all three partners' shares when asked for one. Wastes 30-40 seconds per question. Identify the target partner's fraction (ratio part / total parts) and apply it directly to total profit.
Assuming a working partner automatically gets more. Working partner's salary comes out of profit before division only if the question explicitly states a salary or commission percentage. If the question only gives capital and time, split purely on capital-months — do not add any bonus to the active partner.