Sacrificing ratio: Class 12 practice
When a partner is admitted, old partners give up part of their share. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Fractions
- Profit-sharing ratio
The idea behind sacrificing ratio
When a partner is admitted, old partners give up part of their share. Sacrificing ratio = old ratio − new ratio for each old partner. Goodwill brought by the new partner is shared in this ratio.
Step-by-step method
- Write old and new shares with a common denominator.
- Sacrifice = old − new.
- Simplify the ratio of sacrifices.
Worked example 1 (Basic)
A and B share profits 2 : 1. C is admitted for 1/5 share, taken from A and B in their old ratio. Find the new ratio.
- A new = 8/15, B new = 4/15, C = 1/5
- Answer: 8 : 4 : 3
Worked example 2 (Standard)
A and B share profits 2 : 1. C is admitted for 1/4 share, taken from A and B in their old ratio. Find the new ratio and the sacrificing ratio.
- A new = 1/2, B new = 1/4, C = 1/4
- Sacrifice A : B = 2 : 1
- Answer: New 6 : 3 : 3; sacrifice 2 : 1
Worked example 3 (Challenge)
A and B share 2 : 1. C joins for 1/4 and brings ₹4,500 as premium for goodwill. How is it shared?
- Sacrificing ratio = old ratio 2 : 1
- A ₹3,000, B ₹1,500
- Answer: A ₹3,000, B ₹1,500
Common mistakes and misconceptions
- Using the new ratio for goodwill
- Not converting to a common denominator
Practice questions
- (Basic) A and B share profits 5 : 3. C is admitted for 1/4 share, taken from A and B in their old ratio. Find the new ratio.
- (Basic) A and B share profits 1 : 1. C is admitted for 1/6 share, taken from A and B in their old ratio. Find the new ratio.
- (Standard) A and B share profits 3 : 1. C is admitted for 1/3 share, taken from A and B in their old ratio. Find the new ratio and the sacrificing ratio.
- (Standard) A and B share profits 5 : 3. C is admitted for 1/4 share, taken from A and B in their old ratio. Find the new ratio and the sacrificing ratio.
- (Challenge) A and B share 1 : 1. C joins for 1/4 and brings ₹15,000 as premium for goodwill. How is it shared?
- (Challenge) A and B share 1 : 1. C joins for 1/4 and brings ₹4,500 as premium for goodwill. How is it shared?
Answer key with full working
- Q1: A new = 15/32, B new = 9/32, C = 1/4 → Answer: 15 : 9 : 8
- Q2: A new = 5/12, B new = 5/12, C = 1/6 → Answer: 5 : 5 : 2
- Q3: A new = 1/2, B new = 1/6, C = 1/3 → Sacrifice A : B = 3 : 1 → Answer: New 6 : 2 : 4; sacrifice 3 : 1
- Q4: A new = 15/32, B new = 9/32, C = 1/4 → Sacrifice A : B = 5 : 3 → Answer: New 15 : 9 : 8; sacrifice 5 : 3
- Q5: Sacrificing ratio = old ratio 1 : 1 → A ₹7,500, B ₹7,500 → Answer: A ₹7,500, B ₹7,500
- Q6: Sacrificing ratio = old ratio 1 : 1 → A ₹2,250, B ₹2,250 → Answer: A ₹2,250, B ₹2,250
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 sacrificing ratio 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.