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New and sacrificing ratio on admission: Class 12 practice

When a partner joins, old partners give up (sacrifice) part of their share. Read the method, follow the three worked examples, then try the six questions.

What you should know first

  • Fractions
  • Ratios

The idea behind new and sacrificing ratio on admission

When a partner joins, old partners give up (sacrifice) part of their share. New ratio = old share − sacrifice for each old partner, plus the newcomer's share. Sacrificing ratio = old share − new share.

Step-by-step method

  1. Write old shares as fractions.
  2. Remaining share for old partners = 1 − new partner's share.
  3. If sacrificed in old ratio, multiply old shares by the remaining share.
  4. Sacrifice = old − new.

Worked example 1 (Basic)

A and B share profits 3 : 1. C is admitted for a 1/3 share, taken from A and B in their old ratio. Find the new ratio.

  1. Remaining for A and B = 2/3
  2. A = 3/4 × 2/3 = 6/12; B = 2/12; C = 4/12
  3. Answer: 3 : 1 : 2

Worked example 2 (Standard)

A and B share profits 2 : 1. C is admitted for a 1/4 share, taken from A and B in their old ratio. Find the new ratio.

  1. Remaining for A and B = 3/4
  2. A = 2/3 × 3/4 = 6/12; B = 3/12; C = 3/12
  3. Answer: 2 : 1 : 1

Worked example 3 (Challenge)

A and B share profits 1 : 1. C is admitted for 1/4 share taken from A and B in their old ratio. Find the sacrificing ratio.

  1. New: 3/8, 3/8
  2. Sacrifice A = 1/2 − 3/8 = 1/8, B = 1/8
  3. Answer: 1 : 1

Common mistakes and misconceptions

  • Forgetting the new partner's share in the total
  • Sacrifice computed as new − old

Practice questions

  1. (Basic) A and B share profits 5 : 3. C is admitted for a 1/4 share, taken from A and B in their old ratio. Find the new ratio.
  2. (Basic) A and B share profits 1 : 1. C is admitted for a 1/5 share, taken from A and B in their old ratio. Find the new ratio.
  3. (Standard) A and B share profits 3 : 2. C is admitted for a 1/4 share, taken from A and B in their old ratio. Find the new ratio.
  4. (Standard) A and B share profits 4 : 1. C is admitted for a 1/6 share, taken from A and B in their old ratio. Find the new ratio.
  5. (Challenge) A and B share profits 1 : 1. C is admitted for 1/3 share taken from A and B in their old ratio. Find the sacrificing ratio.
  6. (Challenge) A and B share profits 4 : 1. C is admitted for 1/3 share taken from A and B in their old ratio. Find the sacrificing ratio.

Answer key with full working

  • Q1: Remaining for A and B = 3/4 → A = 5/8 × 3/4 = 15/32; B = 9/32; C = 8/32 → Answer: 15 : 9 : 8
  • Q2: Remaining for A and B = 4/5 → A = 1/2 × 4/5 = 4/10; B = 4/10; C = 2/10 → Answer: 2 : 2 : 1
  • Q3: Remaining for A and B = 3/4 → A = 3/5 × 3/4 = 9/20; B = 6/20; C = 5/20 → Answer: 9 : 6 : 5
  • Q4: Remaining for A and B = 5/6 → A = 4/5 × 5/6 = 20/30; B = 5/30; C = 5/30 → Answer: 4 : 1 : 1
  • Q5: New: 2/6, 2/6 → Sacrifice A = 1/2 − 2/6 = 1/6, B = 1/6 → Answer: 1 : 1
  • Q6: New: 8/15, 2/15 → Sacrifice A = 4/5 − 8/15 = 4/15, B = 1/15 → Answer: 4 : 1

Syllabus note

This skill is listed under "Admission of a Partner" for Class 12 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

Related practice and notes

Frequently asked questions

Which chapter is new and sacrificing ratio on admission in?

"Admission of a Partner", Class 12 Accountancy (NCERT/CBSE). Other boards may place it differently.

How were the answers checked?

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

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