Partnership: Joining Later, Changing Capital and Working Partners
Partnership: Joining Later, Changing Capital and Working Partners
Real businesses change: a partner joins after some months, another adds or withdraws money midway, or one partner runs the business and takes a salary first. Each of these is still capital × months, added piece by piece, with any salary or commission taken out before the rest is shared.
1. Rules Box
Partner joining after m months (12-month year): his capital counts for (12 − m) months
Capital changed midway: add the products piece by piece, e.g. C₁ × (first months) + C₂ × (remaining months)
Working partner: deduct the salary or commission from the profit first, share the rest by capital × time, then add the salary to the working partner's share
Sleeping partner: invests but does not work; gets only the capital share
| Situation | Effective investment |
|---|---|
| ₹60,000, withdraws ₹20,000 after 4 months | 60 × 4 + 40 × 8 = 560 (thousand-months) |
| ₹45,000, adds ₹15,000 after 3 months | 45 × 3 + 60 × 9 = 675 |
| Joins after 6 months with ₹80,000 | 80 × 6 = 480 |
✗ B joins after 4 months, so his capital counts for 4 months | ✓ It counts for the remaining 12 − 4 = 8 months
✗ The working partner's 10% salary is shared with the others too | ✓ Take it out first; share only the remaining 90%
हिंदी नोट: बाद में जुड़ने वाले साझेदार की पूँजी बचे हुए महीनों के लिए गिनी जाती है। बीच में पूँजी बदले तो हर हिस्से का पूँजी × महीने अलग जोड़िए। कार्यकारी साझेदार का वेतन पहले घटाइए, फिर बचा लाभ बाँटिए।
Exam Pointer: Verified NTPC pattern: a third partner joining after six months, with the year-end profit ratio asked (March 2026 Graduate CBT-1). Midway withdrawal, working-partner and unknown-capital questions had no verified NTPC shift in our check and are tagged syllabus-based.
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: A partner joins later
[PYQ: NTPC Graduate CBT-1 25-Mar-2026 Shift-3]
EXAM LEVEL
Q. A starts a business with ₹50,000. After 4 months B joins with ₹60,000. Divide a year-end profit of ₹27,000.
A: 50 × 12 = 600; B: 60 × 8 = 480. Ratio 5 : 4, so A gets ₹15,000 and B ₹12,000.
Answer: A ₹15,000, B ₹12,000
EXAMATLAS LEVEL
Q. A and B start a business with ₹40,000 and ₹60,000. After 6 months C joins with ₹80,000. Find the profit-sharing ratio and C's share of a year-end profit of ₹56,000.
A: 40 × 12 = 480; B: 60 × 12 = 720; C: 80 × 6 = 480. Ratio 2 : 3 : 2, seven parts of ₹8,000, so C gets ₹16,000.
Answer: 2 : 3 : 2; ₹16,000
Pattern 2: Capital added or withdrawn midway
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. A invests ₹60,000 and withdraws ₹20,000 after 4 months. B invests ₹50,000 for the whole year. Find A's share of a profit of ₹58,000.
A: 60 × 4 + 40 × 8 = 560; B: 50 × 12 = 600. Ratio 14 : 15, so A gets 58,000 × 14/29 = ₹28,000.
Answer: ₹28,000
EXAMATLAS LEVEL
Q. A and B start with ₹45,000 and ₹60,000. After 3 months A adds ₹15,000, and after 6 months B withdraws ₹20,000. Divide a year-end profit of ₹34,000.
A: 45 × 3 + 60 × 9 = 675; B: 60 × 6 + 40 × 6 = 600. Ratio 9 : 8, seventeen parts of ₹2,000: A ₹18,000 and B ₹16,000.
Answer: A ₹18,000, B ₹16,000
Pattern 3: Working partner with a salary or commission
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. A is a sleeping partner and B a working partner who gets 10% of the profit for managing. The rest is shared in the capital ratio 3 : 2. Find B's total from a profit of ₹50,000.
B's commission = ₹5,000. The remaining ₹45,000 is shared 27,000 : 18,000. B gets 5,000 + 18,000 = ₹23,000.
Answer: ₹23,000
EXAMATLAS LEVEL
Q. A and B invest ₹50,000 and ₹30,000 for a year. B manages the business and draws ₹1,000 a month as salary. The year's profit before salary is ₹40,000. How much does each receive, and how much more does B get than A?
Salary = ₹12,000, leaving ₹28,000 to share 5 : 3: A ₹17,500 and B ₹10,500. B's total = 10,500 + 12,000 = ₹22,500, which is ₹5,000 more than A.
Answer: A ₹17,500, B ₹22,500; ₹5,000
Pattern 4: Unknown capital from a share
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. A invests ₹25,000 for 12 months and B invests some money for 8 months. Of a profit of ₹18,000, B gets ₹8,000. Find B's investment.
Shares 10,000 : 8,000 = 5 : 4. So 25,000 × 12 : 8x = 5 : 4, giving 40x = 12,00,000 and x = ₹30,000.
Answer: ₹30,000
EXAMATLAS LEVEL
Q. A invests twice as much as B, and B three times as much as C. A's money stays for 4 months, B's for 6 months and C's for 12 months. Find B's share of a profit of ₹27,000.
Take C = 1, B = 3, A = 6. Products: 6 × 4 = 24, 3 × 6 = 18, 1 × 12 = 12, a ratio of 4 : 3 : 2. B gets 3/9 of 27,000 = ₹9,000.
Answer: ₹9,000
60-Second Revision
- Joining after m months: capital × (12 − m).
- Midway change: add each piece's capital × months.
- Salary or commission first, then share the rest.
- Unknown capital: set the capital × time ratio equal to the profit ratio.
Next Step: Partnership done. Practise the partnership set in the ExamAtlas RRB NTPC 2026 mock tests; write every partner's capital × months in one line and the ratio is ready.