New Profit Sharing Ratio on Admission of a Partner: Formulas and Examples

Whenever a new partner joins a firm, one question comes first: how will profits be divided going forward? This is where the new profit sharing ratio comes in. It's one of the most frequently tested numerical topics in CBSE Class 12 Accountancy, and once you understand the logic, the calculations become mechanical and easy to score full marks on.

What Is the New Profit Sharing Ratio?

The new profit sharing ratio is the ratio in which all partners — old and new — will share future profits after a new partner is admitted. Since the new partner's share has to come from somewhere, the old partners give up, or "sacrifice," a part of their existing share in favour of the incoming partner.

If nothing is specified about how the new partner acquires their share, it is assumed they get it from the old partners in the old partners' existing profit sharing ratio. This default assumption is important — examiners frequently test whether you know to apply it.

Case 1: New Partner Acquires Share in the Old Ratio

This is the simplest and most common scenario.

Example: Anil and Vishal share profits in the ratio 3:2. They admit Sumit for a 1/5 share in future profits, assumed to come from Anil and Vishal in their old ratio.

Step 1: Sumit's share = 1/5
Step 2: Remaining share for Anil and Vishal = 1 − 1/5 = 4/5
Step 3: Anil's new share = 3/5 × 4/5 = 12/25
Step 4: Vishal's new share = 2/5 × 4/5 = 8/25
Step 5: Sumit's share expressed with the same denominator = 5/25

New ratio of Anil : Vishal : Sumit = 12 : 8 : 5

Case 2: New Partner Acquires Share in a Specified Ratio From Old Partners

Sometimes the question tells you exactly how much the new partner takes from each old partner.

Example: Meera and Kunal share profits 3:2. They admit Rhea for a 1/5 share, which she acquires equally from Meera and Kunal.

  • Rhea's share = 1/5 = 2/10
  • Amount taken from each = 1/10
  • Meera's new share = 3/5 − 1/10 = 6/10 − 1/10 = 5/10
  • Kunal's new share = 2/5 − 1/10 = 4/10 − 1/10 = 3/10

New ratio of Meera : Kunal : Rhea = 5 : 3 : 2

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Case 3: Old Partners Surrender a Fraction of Their Own Share

In this variation, each old partner sacrifices a stated fraction of their own existing share, not a fraction of the total business.

Example: Ram and Shyam share profits 3:2. They admit a new partner, and Ram sacrifices 1/4 of his own share while Shyam sacrifices 1/3 of his own share.

  • Ram's sacrifice = 1/4 of 3/5 = 3/20
  • Ram's new share = 3/5 − 3/20 = 12/20 − 3/20 = 9/20
  • Shyam's sacrifice = 1/3 of 2/5 = 2/15
  • Shyam's new share = 2/5 − 2/15 = 6/15 − 2/15 = 4/15
  • New partner's share = Ram's sacrifice + Shyam's sacrifice = 3/20 + 2/15 = 9/60 + 8/60 = 17/60

Converting everything to a denominator of 60: Ram = 27/60, Shyam = 16/60, new partner = 17/60.

New ratio = 27 : 16 : 17

Case 4: Total Share Is Surrendered Entirely by One Partner

Occasionally, only one old partner sacrifices, while the other's share stays untouched.

Example: Das and Sinha share profits 4:1. They admit Pal for a 1/4 share, which Pal acquires wholly from Das.

  • Das's new share = 4/5 − 1/4 = 16/20 − 5/20 = 11/20
  • Sinha's share remains = 1/5 = 4/20
  • Pal's share = 1/4 = 5/20

New ratio of Das : Sinha : Pal = 11 : 4 : 5

A Quick Method to Avoid Errors

The safest way to solve any new profit sharing ratio problem is:

  1. Write down the new partner's share as given.
  2. Determine exactly how much each old partner is giving up (look for keywords like "equally," "in old ratio," "surrenders 1/4 of his share").
  3. Subtract the sacrifice from each old partner's original share.
  4. Express all resulting fractions with a common denominator.
  5. Write the final ratio using whole numbers.

Skipping step 4 is the single biggest reason students lose marks — always convert to a common denominator before writing your final answer.

Why This Concept Matters Beyond the Exam

The new profit sharing ratio isn't just an exam formality. It determines exactly how much of every future rupee of profit each partner is entitled to, and it directly feeds into calculating the sacrificing ratio, which in turn decides how goodwill compensation is split among old partners. Get this step wrong, and every subsequent calculation in the question — goodwill, capital adjustment, everything — goes wrong too.

  • Link "reconstitution of the partnership" to Reconstitution of a Partnership Firm: Meaning and Modes
  • Link "sacrificing ratio" to Sacrificing Ratio in Partnership Accounts
  • Link "goodwill compensation" to Accounting Treatment of Goodwill on Admission of a Partner
  • Add a link to ChampionsPrep's Class 12 Accountancy MCQ practice set on profit sharing ratios

Practice Makes This Topic Effortless

New profit sharing ratio questions are formula-driven — the more variations you practise, the faster you become. ChampionsPrep offers pay-per-use practice sets on this exact topic for CBSE and State Board Class 12 Commerce students. Try a set today and build exam-day speed.

Test Your Knowledge

Interactive Practice: Identify the Accounting Concept

1.Personal travel expenses of the owner paid from business cash are debited to Drawings A/c
2.The high skill, dedication, and morale of the sales team are not recorded in books
3.Fixed assets are recorded at cost less depreciation rather than immediate net realizable liquidation value
WORKED EXAMPLE · Admission of Partner: Calculating New Profit Sharing Ratio
Anil and Vishal are partners sharing profits in the ratio of 3:2. They admit Sumit into the partnership for a 1/5th share in future profits. Calculate the new profit sharing ratio of Anil, Vishal, and Sumit.
Work through each sequential step to determine how the sacrifice is distributed and the new ratio is formed:
Step 1: Identify New Partner's Share & Remaining Profit
Total Share=1,Sumit’s Share=15,Remaining Share=1−15=45\text{Total Share} = 1, \quad \text{Sumit's Share} = \frac{1}{5}, \quad \text{Remaining Share} = 1 - \frac{1}{5} = \frac{4}{5}
Assuming the total future profit is 1, deducting Sumit's 1/5 share leaves 4/5 to be divided between old partners in their old ratio (3:2).
Step 2: Calculate Anil's New Share
Anil’s New Share=35×45=1225\text{Anil's New Share} = \frac{3}{5} \times \frac{4}{5} = \frac{12}{25}
Anil takes 3/5 of the remaining 4/5 profit pool.
Step 3: Calculate Vishal's New Share
Vishal’s New Share=25×45=825\text{Vishal's New Share} = \frac{2}{5} \times \frac{4}{5} = \frac{8}{25}
Vishal takes 2/5 of the remaining 4/5 profit pool.
Step 4: Express Incoming Partner's Share with Common Denominator
Sumit’s Share=15=1×55×5=525\text{Sumit's Share} = \frac{1}{5} = \frac{1 \times 5}{5 \times 5} = \frac{5}{25}
To compare all shares directly, convert Sumit's 1/5 to denominator 25.
Step 5: Final Ratio Formulation
Anil : Vishal : Sumit=1225:825:525  ⟹  12:8:5\text{Anil : Vishal : Sumit} = \frac{12}{25} : \frac{8}{25} : \frac{5}{25} \implies 12 : 8 : 5
Sum of numerators = 12 + 8 + 5 = 25. The new profit sharing ratio is 12:8:5.
Solution Complete!
All 5 steps revealed and verified.

Frequently Asked Questions

What is the new profit sharing ratio? +

It is the ratio in which all partners, including the newly admitted one, will share the firm's profits after the reconstitution of the partnership.

What happens if a question doesn't specify how the new partner acquires their share? +

It is assumed the new partner acquires their share from the old partners in their existing (old) profit sharing ratio.

Can the new partner acquire their entire share from just one old partner? +

Yes. If the question states this explicitly, only that one partner's share is reduced, while other old partners' shares remain unchanged.

Why is expressing shares with a common denominator important? +

Without a common denominator, the fractions cannot be compared or combined correctly, which leads to an incorrect final ratio.

How is the new profit sharing ratio related to the sacrificing ratio? +

The sacrificing ratio is calculated as the old share minus the new share for each old partner, so you generally need the new ratio first before working out the sacrificing ratio.

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