Gaining ratio on retirement: Class 12 practice
When a partner retires, the others gain his share. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Fractions
The idea behind gaining ratio on retirement
When a partner retires, the others gain his share. Gaining ratio = new share − old share for each continuing partner. If no new ratio is given, they continue in their old ratio between themselves.
Step-by-step method
- Write old shares.
- Find new shares (given or old ratio between continuing partners).
- Gain = new − old.
Worked example 1 (Basic)
A, B and C share profits 2 : 2 : 1. C retires and A and B continue in their old ratio. Find the gaining ratio.
- New: A 2/4, B 2/4
- Gain A = 1/10, B = 1/10
- Answer: 1 : 1
Worked example 2 (Standard)
A, B and C share profits 1 : 1 : 1. C retires and A and B agree to share 1 : 1. Find the gaining ratio.
- New: A 1/2, B 1/2
- Gain A = 1/6, B = 1/6
- Answer: 1 : 1
Worked example 3 (Challenge)
A, B and C share profits 4 : 3 : 2. C retires and A and B agree to share 3 : 2. Find the gaining ratio.
- New: A 3/5, B 2/5
- Gain A = 7/45, B = 1/15
- Answer: 7 : 3
Common mistakes and misconceptions
- Using the old ratio of all three
- Gain computed as old − new
Practice questions
- (Basic) A, B and C share profits 3 : 2 : 1. C retires and A and B continue in their old ratio. Find the gaining ratio.
- (Basic) A, B and C share profits 5 : 3 : 2. C retires and A and B continue in their old ratio. Find the gaining ratio.
- (Standard) A, B and C share profits 1 : 1 : 1. C retires and A and B agree to share 3 : 1. Find the gaining ratio.
- (Standard) A, B and C share profits 1 : 1 : 1. C retires and A and B agree to share 2 : 1. Find the gaining ratio.
- (Challenge) A, B and C share profits 5 : 3 : 2. C retires and A and B agree to share 3 : 1. Find the gaining ratio.
- (Challenge) A, B and C share profits 4 : 3 : 2. C retires and A and B agree to share 1 : 1. Find the gaining ratio.
Answer key with full working
- Q1: New: A 3/5, B 2/5 → Gain A = 1/10, B = 1/15 → Answer: 3 : 2
- Q2: New: A 5/8, B 3/8 → Gain A = 1/8, B = 3/40 → Answer: 5 : 3
- Q3: New: A 3/4, B 1/4 → Gain A = 5/12, B = -1/12 → Answer: A 5/12, B -1/12
- Q4: New: A 2/3, B 1/3 → Gain A = 1/3, B = 0 → Answer: A 1/3, B 0
- Q5: New: A 3/4, B 1/4 → Gain A = 1/4, B = -1/20 → Answer: A 1/4, B -1/20
- Q6: New: A 1/2, B 1/2 → Gain A = 1/18, B = 1/6 → Answer: 1 : 3
Syllabus note
This skill is listed under "Retirement and Death 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 gaining ratio on retirement in?
"Retirement and Death 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.