Class 9 Accountancy Chapter 3: Reconstitution of Partnership Firm — Admission | Important Questions & Solutions

The CBSE Class 9 Accountancy syllabus (2024-25 rationalized) places Reconstitution of Partnership Firm — Admission as a foundational pillar for accounting mechanics. In recent years, the board has shifted from pure definition-based questions to calculation-heavy, scenario-driven problems that test your ability to compute new profit ratios, identify sacrificing partners, and account for goodwill. The 2026-27 pattern is expected to strengthen this trend. Questions now frequently present real-world situations: 'A, B, and C were partners sharing profits in 2:3:5. C retires and D is admitted. Calculate the new ratio and sacrificing ratio.' Such multi-step problems account for 60% of board marks in this chapter. Understanding the conceptual logic — why we calculate sacrificing ratio, how goodwill affects capital accounts, and the journal entries required — is now non-negotiable. Students who can link formula application to real scenarios score 8+ out of 10. This curated set of 17 questions covers every subtopic and difficulty tier, ensuring you're ready for both expected and surprise questions.

MCQs in CBSE Class 9 Accountancy test quick conceptual recall and formula familiarity. Here are 5 board-pattern MCQs: **Q1.** When a new partner is admitted, the sacrificing ratio is calculated as: (A) Old ratio + New ratio (B) Old ratio − New ratio (C) New ratio / Old ratio (D) Old ratio × New ratio **Answer: (B)** Old ratio − New ratio. Sacrificing ratio represents the share of profit each old partner surrenders to the new partner. **Q2.** If A, B, C share profits in 3:2:1 and D is admitted for 1/6 share, the new ratio is: (A) 3:2:1:1 (B) 5:4:2:1 (C) 6:4:2:1 (D) 9:6:3:2 **Answer: (D)** 9:6:3:2. Remaining share = 1 − 1/6 = 5/6. Divide in old ratio 3:2:1 → (3/6)×(5/6) : (2/6)×(5/6) : (1/6)×(5/6) = 5:10:5 (in terms of 18 parts) = 9:6:3:2 after adjusting. **Q3.** Goodwill is an intangible asset that appears on the balance sheet when: (A) A partner retires (B) A new partner is admitted and pays a premium (C) A partnership dissolves (D) The firm makes a profit **Answer: (B)** A new partner is admitted and pays a premium. The premium paid for goodwill is recorded as an asset or credited to old partners' capital. **Q4.** If the sacrificing ratio of two partners is 2:1, it means: (A) One partner sacrificed twice the profit share of the other (B) The new partner's share is in ratio 2:1 (C) The new profit ratio is 2:1 (D) The old profit ratio was 2:1 **Answer: (A)** One partner sacrificed twice the profit share of the other. This is the literal definition of sacrificing ratio. **Q5.** On admission of a new partner, if goodwill is written off, the journal entry is: (A) Debit Goodwill, Credit Partners' Capital (B) Debit Partners' Capital, Credit Goodwill (C) Debit New Partner's Capital, Credit Goodwill (D) Debit Profit & Loss, Credit Goodwill **Answer: (A)** Debit Goodwill, Credit Partners' Capital. Old partners share the goodwill write-off in their sacrificing ratio.

2-mark questions test definition-level understanding and simple calculations. Here are 5 board-aligned examples: **Q1. Define sacrificing ratio and explain why it is calculated when a new partner is admitted.** *Answer (40 words):* Sacrificing ratio is the proportion in which old partners reduce their profit-sharing ratio to accommodate the new partner. It is calculated to determine how much profit each old partner surrenders and ensures fair compensation through goodwill payments. Example: If A's share reduces from 1/2 to 2/5, A sacrifices 1/2 − 2/5 = 1/10. **Q2. X and Y are partners with profit-sharing ratio 3:2. Z is admitted for 1/5 share. Calculate the new profit-sharing ratio.** *Answer:* Remaining share after Z's admission = 1 − 1/5 = 4/5. This is divided among X and Y in their old ratio 3:2. X's new share = (3/5) × (4/5) = 12/25. Y's new share = (2/5) × (4/5) = 8/25. Z's share = 1/5 = 5/25. New ratio = 12:8:5. **Q3. What is goodwill and how does it arise in a partnership firm?** *Answer (50 words):* Goodwill is the reputation, customer base, and earning capacity a business has built over time. In partnerships, it arises when a new partner is admitted and pays a premium above capital investment, or when an existing partnership has sustained above-average profits. It is an intangible asset valued using average profit or capitalization methods. **Q4. P and Q share profits equally. R is admitted such that the new ratio becomes 2:2:1. Calculate the sacrificing ratio.** *Answer:* Old ratio = 1:1. New ratio = 2:2:1. Sacrificing ratio = Old − New. P sacrifices = 1/2 − 2/5 = 1/10. Q sacrifices = 1/2 − 2/5 = 1/10. Sacrificing ratio = 1:1. **Q5. If goodwill of a firm is valued at ₹50,000 and a new partner contributes 1/4 of this amount to old partners, show the journal entry.** *Answer:* Goodwill value = ₹50,000. New partner's contribution = 1/4 × 50,000 = ₹12,500. Journal entry: Debit Bank/Cash ₹12,500, Credit Old Partners' Capital ₹12,500 (in sacrificing ratio). This ensures old partners are compensated for surrendered profit.

3-mark questions require multi-step calculations and journal entries. Here are 4 representative questions: **Q1. A and B are partners with profit-sharing ratio 3:2. C is admitted for 1/4 share. Goodwill is valued at ₹40,000. Pass journal entries if goodwill is brought in by the new partner.** *Solution:* Step 1: New ratio. Remaining share = 1 − 1/4 = 3/4. A's new share = (3/5) × (3/4) = 9/20. B's new share = (2/5) × (3/4) = 6/20 = 3/10. C's share = 1/4 = 5/20. New ratio = 9:6:5. Step 2: Sacrificing ratio = Old − New. A: 3/5 − 9/20 = 3/20. B: 2/5 − 6/20 = 2/20 = 1/10. Sacrificing ratio = 3:2. Step 3: C's goodwill contribution = 1/4 × 40,000 = ₹10,000. Journal entries: (1) Bank Dr. 10,000 / To A's Capital Cr. 6,000 / To B's Capital Cr. 4,000 [goodwill in sacrificing ratio 3:2] (2) C's Capital Dr. (for other capital brought) / To Bank Cr. **Q2. M, N, O share profits in 5:3:2. P is admitted for 1/5 share such that N and O sacrifice equally. Calculate new ratio and sacrificing ratio.** *Solution:* Step 1: Old ratio = 5:3:2 (total 10). P's share = 1/5 = 2/10. Remaining = 8/10. Step 2: N and O sacrifice equally. Total sacrifice = 2/10. Each sacrifices 1/10. Step 3: M's new share = 5/10 (unchanged) = 5/10. N's new share = 3/10 − 1/10 = 2/10. O's new share = 2/10 − 1/10 = 1/10. P's share = 2/10. New ratio = 5:2:1:2. Step 4: Sacrificing ratio = M: 0, N: 1/10, O: 1/10 = 0:1:1 or simply N and O in ratio 1:1. **Q3. X, Y, Z are partners sharing profits equally. A is admitted for 1/6 share and pays ₹15,000 as goodwill premium. Goodwill is credited to old partners. Pass journal entries.** *Solution:* Step 1: Old ratio = 1:1:1. A's share = 1/6. Remaining = 5/6. X, Y, Z's new shares = (1/3) × (5/6) = 5/18 each. A's share = 3/18. New ratio = 5:5:5:3. Step 2: Sacrificing ratio = 1/3 − 5/18 = 1/18 each for X, Y, Z = 1:1:1. Step 3: A's goodwill ₹15,000 shared in sacrificing ratio 1:1:1. Journal entries: (1) Bank Dr. 15,000 / To X's Capital Cr. 5,000 / To Y's Capital Cr. 5,000 / To Z's Capital Cr. 5,000 (2) A's Capital Dr. (for capital contributed) / To Bank Cr. **Q4. D, E, F were sharing profits in 2:3:5. G is admitted for 1/4 share on condition that D, E, F sacrifice in the ratio 1:1:2 respectively. Calculate the new profit-sharing ratio.** *Solution:* Step 1: Old ratio = 2:3:5 (total 10 parts). G's share = 1/4 = 2.5/10. Remaining = 7.5/10. Step 2: Sacrificing ratio = 1:1:2. D sacrifices 1/4 part, E sacrifices 1/4, F sacrifices 1/2. Total sacrifice = 1 part. Step 3: D's new share = 2/10 − (1/4 × 1/10) = 2/10 − 1/40 = 7/40. E's new share = 3/10 − 1/40 = 11/40. F's new share = 5/10 − 2/40 = 18/40. G's share = 1/4 = 10/40. New ratio = 7:11:18:10.

5-mark questions test comprehensive understanding, multiple calculations, and detailed journal entries. Here are 3 complete solutions: **Q1. A and B are partners in a firm. Their profit-sharing ratio is 3:2. They decide to admit C for 1/4 share in profits. C will bring capital of ₹50,000 and will pay ₹10,000 as goodwill premium. The goodwill of the firm is valued at ₹40,000. Pass all journal entries for the admission of C and prepare the new capital accounts.** *Complete Solution:* Step 1: Calculate New Profit-Sharing Ratio Old ratio (A : B) = 3:2. C's share = 1/4. Remaining share = 3/4. A's new share = (3/5) × (3/4) = 9/20 B's new share = (2/5) × (3/4) = 6/20 = 3/10 C's share = 1/4 = 5/20 New ratio = 9:6:5 Step 2: Calculate Sacrificing Ratio A's sacrifice = 3/5 − 9/20 = 12/20 − 9/20 = 3/20 B's sacrifice = 2/5 − 6/20 = 8/20 − 6/20 = 2/20 = 1/10 Sacrificing ratio (A : B) = 3/20 : 1/10 = 3:2 Step 3: Goodwill Treatment C pays goodwill premium = ₹10,000 This is shared among A and B in sacrificing ratio 3:2 A receives = (3/5) × 10,000 = ₹6,000 B receives = (2/5) × 10,000 = ₹4,000 Step 4: Journal Entries (1) Bank Dr. 10,000 To A's Capital Cr. 6,000 To B's Capital Cr. 4,000 (Goodwill premium brought by C) (2) Bank Dr. 50,000 To C's Capital Cr. 50,000 (Capital brought by C) (3) Goodwill Dr. 40,000 To A's Capital Cr. 24,000 To B's Capital Cr. 16,000 (Goodwill valued at ₹40,000 and credited to A and B in sacrificing ratio 3:2) Alternative: If goodwill is written off immediately: A's Capital Dr. 24,000 B's Capital Dr. 16,000 To Goodwill Cr. 40,000 **Q2. X, Y, Z are partners sharing profits in ratio 4:3:1. They admit W for 1/6 share. W brings capital of ₹60,000 and goodwill of ₹18,000. The firm's goodwill is valued at ₹36,000. Pass journal entries and show capital accounts after admission (assume old partners' capitals remain unchanged).** *Complete Solution:* Step 1: New Profit-Sharing Ratio Old ratio (X : Y : Z) = 4:3:1 (total 8). W's share = 1/6. Remaining = 5/6. X's new share = (4/8) × (5/6) = 20/48 = 5/12 Y's new share = (3/8) × (5/6) = 15/48 = 5/16 Z's new share = (1/8) × (5/6) = 5/48 W's share = 1/6 = 8/48 New ratio = 20:15:5:8 Step 2: Sacrificing Ratio X's sacrifice = 4/8 − 5/12 = 12/24 − 10/24 = 2/24 = 1/12 Y's sacrifice = 3/8 − 5/16 = 6/16 − 5/16 = 1/16 Z's sacrifice = 1/8 − 5/48 = 6/48 − 5/48 = 1/48 Sacrificing ratio = 1/12 : 1/16 : 1/48 = 4:3:1 (LCM 48) Step 3: Goodwill Accounting W's goodwill contribution = ₹18,000 This is distributed to X, Y, Z in sacrificing ratio 4:3:1 X receives = (4/8) × 18,000 = ₹9,000 Y receives = (3/8) × 18,000 = ₹6,750 Z receives = (1/8) × 18,000 = ₹2,250 Step 4: Journal Entries (1) Bank Dr. 18,000 To X's Capital Cr. 9,000 To Y's Capital Cr. 6,750 To Z's Capital Cr. 2,250 (Goodwill premium by W in sacrificing ratio) (2) Bank Dr. 60,000 To W's Capital Cr. 60,000 (Capital brought by W) (3) Goodwill Dr. 36,000 To X's Capital Cr. 18,000 To Y's Capital Cr. 13,500 To Z's Capital Cr. 4,500 (Goodwill valued and credited in sacrificing ratio 4:3:1) **Q3. P, Q, R are partners with capital accounts showing ₹1,00,000, ₹80,000, ₹60,000 respectively. Their profit-sharing ratio is 2:2:1. S is admitted for 1/5 share and brings capital equal to ₹50,000. Calculate the new profit-sharing ratio, sacrificing ratio, and goodwill of the firm (using capital method). Pass journal entries for goodwill treatment if old partners decide to write off goodwill from their capital accounts.** *Complete Solution:* Step 1: New Profit-Sharing Ratio Old ratio (P : Q : R) = 2:2:1. S's share = 1/5. Remaining = 4/5. P's new share = (2/5) × (4/5) = 8/25 Q's new share = (2/5) × (4/5) = 8/25 R's new share = (1/5) × (4/5) = 4/25 S's share = 1/5 = 5/25 New ratio = 8:8:4:5 Step 2: Sacrificing Ratio P's sacrifice = 2/5 − 8/25 = 10/25 − 8/25 = 2/25 Q's sacrifice = 2/5 − 8/25 = 2/25 R's sacrifice = 1/5 − 4/25 = 5/25 − 4/25 = 1/25 Sacrificing ratio = 2:2:1 Step 3: Goodwill Calculation (Capital Method) Total capital after S's admission = 1,00,000 + 80,000 + 60,000 + 50,000 = ₹2,90,000 S's share = 1/5, so S's capital ₹50,000 represents 1/5 of total. If ₹50,000 = 1/5, then total capital should be 5 × 50,000 = ₹2,50,000 Implied total capital = ₹2,50,000 (not ₹2,90,000) Difference (Goodwill) = 2,90,000 − 2,50,000 = ₹40,000 Step 4: Journal Entries (Goodwill write-off from capital accounts) (1) Bank Dr. 50,000 To S's Capital Cr. 50,000 (Capital brought by S) (2) P's Capital Dr. 16,000 (2/5 of 40,000) Q's Capital Dr. 16,000 (2/5 of 40,000) R's Capital Dr. 8,000 (1/5 of 40,000) To Goodwill Cr. 40,000 (Goodwill written off in sacrificing ratio 2:2:1) Final Capital Accounts: P: 1,00,000 + 16,000 = ₹1,16,000 (after write-off reduction: ₹84,000) Q: 80,000 + 16,000 = ₹96,000 (after write-off reduction: ₹80,000) R: 60,000 + 8,000 = ₹68,000 (after write-off reduction: ₹60,000) S: 50,000

**Case Study: Admission of a New Partner in a Growing Bakery Business** Rahul and Neha are partners in 'Sweet Delights Bakery,' sharing profits in ratio 3:2. Their firm has generated steady profits of ₹50,000 per annum for the last 3 years. They now want to expand and admit their friend Arjun as a new partner. Arjun will bring capital of ₹1,20,000 and will pay ₹30,000 as goodwill premium. The partners also agree that Arjun will receive 1/4 share in future profits, while Rahul and Neha will adjust their ratio proportionately. The firm decides to value goodwill at ₹60,000 (based on 1.2 years' purchase of average profit). **Tasks (5 marks):** 1. Calculate the new profit-sharing ratio for all three partners. 2. Determine the sacrificing ratio between Rahul and Neha. 3. Analyse how goodwill affects the admission (should old partners write off goodwill or retain it? Justify). 4. Pass journal entries for the admission, assuming goodwill is credited to Rahul and Neha. 5. Calculate the final capital of each partner if Rahul and Neha had initial capitals of ₹2,00,000 and ₹1,50,000 respectively. **Solution with Steps:** **Step 1: New Profit-Sharing Ratio** Old ratio (Rahul : Neha) = 3:2. Arjun's share = 1/4. Remaining = 3/4. Rahul's new share = (3/5) × (3/4) = 9/20 Neha's new share = (2/5) × (3/4) = 6/20 = 3/10 Arjun's share = 1/4 = 5/20 New ratio = 9:6:5 **Step 2: Sacrificing Ratio** Rahul's sacrifice = 3/5 − 9/20 = 12/20 − 9/20 = 3/20 Neha's sacrifice = 2/5 − 6/20 = 8/20 − 6/20 = 2/20 = 1/10 Sacrificing ratio (Rahul : Neha) = 3/20 : 1/10 = 3:2 **Step 3: Goodwill Analysis** Arjun pays ₹30,000 goodwill premium (brought in cash). Firm's goodwill is valued at ₹60,000. Treatment: If goodwill is capitalized, old partners' capitals increase; if written off, it reduces their capital. Since the bakery has consistent profits and goodwill reflects future earning potential, retaining goodwill on the balance sheet is prudent for asset valuation and long-term financing. However, writing it off conservatively reduces inflated balance sheet values. Here, goodwill will be credited to partners' capitals. **Step 4: Journal Entries** (1) Bank Dr. 30,000 To Rahul's Capital Cr. 18,000 To Neha's Capital Cr. 12,000 (Goodwill premium by Arjun in sacrificing ratio 3:2) (2) Bank Dr. 1,20,000 To Arjun's Capital Cr. 1,20,000 (Capital brought by Arjun) (3) Goodwill Dr. 60,000 To Rahul's Capital Cr. 36,000 To Neha's Capital Cr. 24,000 (Goodwill valued at ₹60,000 and credited in sacrificing ratio 3:2) **Step 5: Final Capital Accounts** Rahul: 2,00,000 + 18,000 + 36,000 = ₹2,54,000 Neha: 1,50,000 + 12,000 + 24,000 = ₹1,86,000 Arjun: 1,20,000 **Key Insight:** By admitting Arjun, the bakery doubles its capital base to ₹5,60,000, enabling larger-scale operations and better credit access. The goodwill credit compensates Rahul and Neha fairly for surrendering profit share, ensuring equity among all partners.

Mastering Reconstitution of Partnership Firm — Admission requires more than reading solutions once; it demands daily, targeted practice on the exact question patterns CBSE tests. CBSETUTOR.ai's AI-powered tutor is designed to replicate this precision. Here's how: **Adaptive Question Generation:** The AI analyzes your learning gaps and generates unlimited variations of new profit ratio, sacrificing ratio, and goodwill problems. If you struggle with multi-partner scenarios, the system creates customized 5-partner problems to deepen mastery. **Real-Time Error Detection:** When you solve a 3-mark or 5-mark question, the AI instantly identifies whether your error lies in ratio calculation, sacrificing ratio logic, or journal entry format. It then explains the conceptual reason for the mistake—not just the correct answer. **Board-Pattern Drilling:** The tutor mirrors the exact distribution of 1-mark, 2-mark, 3-mark, and 5-mark questions seen in actual CBSE papers. Daily sessions follow this pattern, ensuring you're exam-ready by the time boards arrive. **Step-by-Step Solution Walkthroughs:** Unlike static textbooks, the AI tutor breaks down each solution into digestible steps with visual aids for capital account preparation and journal entry formats. You can pause, re-read, and ask clarifying questions instantly. **Progress Tracking:** After each daily drill, the system generates a confidence score for new profit ratio, sacrificing ratio, and goodwill separately. You can see which subtopic needs more attention and focus accordingly. **Speed Optimization:** CBSE exams test both accuracy and speed. The AI tutor includes timed quizzes where you solve questions under exam conditions, building both speed and accuracy simultaneously. With CBSETUTOR.ai, you're not just reading Chapter 3 questions—you're drilling the exact patterns that appear in actual board exams, every single day. This approach has helped thousands of Class 9 students move from confusion to 9–10 out of 10 in Accountancy.