Aptitude · Partnerships · Model 4
The manager is paid before the split, not out of it
A working partner runs the business as well as funding it, so they take a salary or a percentage of the profit first. Only what is left goes into the capital × time split. Doing those two steps in the wrong order gives a different answer that still adds up correctly.
Set the cut and see both orders side by side →01 The idea
Two kinds of partner, two kinds of income
A sleeping partner puts money in and does no work. Their income is their share of the profit and nothing else. A working partner puts money in and also runs the business, so they are paid twice: a wage for the work and a share for the capital.
The wage comes out first. Amit and Sumit invest ₹60,000 and ₹40,000, Amit manages the shop for 10% of the profit, and the year’s profit is ₹20,000. Amit’s fee is ₹2,000, so ₹18,000 is left. That ₹18,000 — not the ₹20,000 — is what the 3 : 2 capital ratio divides.
Amit takes three-fifths of ₹18,000, which is ₹10,800, and adds the ₹2,000 fee for a total income of ₹12,800. Sumit takes two-fifths, ₹7,200, and that is all Sumit gets.
Now do it in the wrong order. Split the whole ₹20,000 in 3 : 2 and you get ₹12,000 and ₹8,000. That looks fine: the two figures add to ₹20,000, both partners are paid, nothing is missing. It is also wrong by ₹800 each way, and no sum check will ever find it. This is why the order is the lesson.
02 Worked example
Amit manages the shop for 10% of ₹20,000
This sum runs through the whole lesson. Amit and Sumit invest ₹60,000 and ₹40,000. Amit is the working partner and takes 10% of the total profit as a management fee. The profit is ₹20,000. Find each partner’s total income.
| Order of operations | Amit | Sumit | Total |
|---|---|---|---|
| Cut first, then split — correct | ₹12,800 | ₹7,200 | ₹20,000 |
| Split first, fee treated as inside the share | ₹12,000 | ₹8,000 | ₹20,000 |
| Difference | −₹800 | +₹800 | ₹0 |
Both orders produce two numbers that sum to ₹20,000, so the usual sanity check passes either way. The only defence is the order itself: the cut is a cost of the business and comes out before the owners divide anything. Note also which direction the error runs — splitting first underpays the manager, because it silently makes the sleeping partner share the wage.
03 The method
The formula, and the percentage trick for reverse questions
Two shapes of question. Forward ones give you the profit; reverse ones give you an income and want the profit, and there the whole sum is best done in percentages.
| How the cut is stated | Annual cut | Watch for |
|---|---|---|
| 10% of the total profit | 0.10 × profit | of the total, not the rest |
| ₹1,000 per month | 1,000 × 12 = 12,000 | multiply by 12 first |
| One-sixth of the profit | profit / 6 | a fraction, same treatment |
| Both partners draw a salary | add the salaries | then split what remains |
| Commission on the remainder | read the base | not the same as % of profit |
| Split first, then deduct | wrong order | still sums to the profit |
05 Cheat sheet
Model 4 on one page
The order, the two ways a cut is stated, and the closed form for the equal-income question.
| Case | Rule | On the lesson sum |
|---|---|---|
| Order of operations | cut first, then split | 2,000 out, 18,000 shared |
| Working partner’s income | cut + share of remainder | 2,000 + 10,800 = 12,800 |
| Sleeping partner’s income | share of remainder | ₹7,200 |
| Fixed monthly salary | salary × 12 | 1,000 a month → 12,000 |
| Reverse question | call the profit 100% | 20% + 48% = 68% |
| Equal incomes, capitals 1 : n | salary = (n−1)/2n of profit | n = 2 → 25% |
| Split first, then deduct | wrong, and it still adds up | 12,000 vs 12,800 |
06 Where & why
Where this shows up
Model 4 is the one that reflects how real firms actually pay their partners, and the one where exam setters get the most out of a single ordering error.
“A takes 20% as salary and A’s total income is ₹13,600 — find the profit.” Percentages of the profit settle it in one line.
“₹1,000 per month” has to become ₹12,000 before anything else happens. Forgetting the × 12 is the second trap in this model.
“Both receive the same income — what percentage is the salary?” With capitals 1 : n the answer is (n − 1)/2n, which is worth knowing rather than deriving under time pressure.
A deed sets out a partner’s salary and commission as a charge against profit, and only the residue is divided by the profit-sharing ratio. The model is the accounting rule, not an exam invention.
07 Interview questions
What gets asked
Ten, and the second one is the question this whole lesson exists to answer.
What is the difference between a sleeping and a working partner?
Does the manager’s cut come out before or after the profit is split?
Amit and Sumit invest ₹60,000 and ₹40,000; Amit takes 10% of a ₹20,000 profit as a fee. Find both incomes.
What does the wrong order give in that question, and by how much is it out?
The manager gets ₹1,000 per month. What do you do with that?
A and B invest in the ratio 3 : 2; A takes 20% of the profit as salary and A’s total income is ₹13,600. Find the profit.
A invests ₹40,000 and B ₹80,000; A takes a salary and both end up with the same income. What percentage of the profit is the salary?
What if both partners draw a salary?
“Commission on the remaining profit” instead of a percentage of the profit — does that matter?
Is this how real firms pay partners?
08 Practice problems
Six on the order of operations
State the cut before you touch the capital ratio in every one. Three of these run backwards from an income to a profit, where percentages are much faster than rupees.