Question

Hari, Chander, Prakash and Govind were partners in a firm sharing profits and losses in the ratio of 5 : 3 : 1 : 1. On 1st April, 2024, Hari retired and his share was acquired equally by Chander, Prakash and Govind. The new profit sharing ratio of Chander, Prakash and Govind will be:

• A. 7 : 4 : 4
• B. 15 : 8 : 7
• C. 1 : 1 : 1
• D. 16 : 7 : 7

Hint:

When a partner retires and his share is acquired equally by remaining partners, divide the retiring share equally and add it to each continuing partner’s original share.

Answer 1

The Correct Option is A

Step 1: Old ratio = Hari : Chander : Prakash : Govind = 5 : 3 : 1 : 1 
Total parts = \( 5 + 3 + 1 + 1 = 10 \) 
Step 2: Hari’s share = \( \frac{5}{10} = \frac{1}{2} \) 
His share is acquired equally by Chander, Prakash and Govind. So each gets: \[ \frac{1}{2} \div 3 = \frac{1}{6} \] 
Step 3: Remaining partners' new shares:
- Chander: \( \frac{3}{10} + \frac{1}{6} = \frac{18 + 5}{60} = \frac{23}{60} \)
- Prakash: \( \frac{1}{10} + \frac{1}{6} = \frac{6 + 10}{60} = \frac{16}{60} \)
- Govind: \( \frac{1}{10} + \frac{1}{6} = \frac{6 + 10}{60} = \frac{16}{60} \) \[ \text{New Ratio} = 23 : 16 : 16 \] Now simplify this to smallest whole number ratio: - Multiply each term by LCM of denominators (60 not needed here), or use original format:
Let’s express everything in terms of a total of 15 (common multiple of 5 and 10):
Old Ratio = 5 : 3 : 1 : 1 → Multiply by 3 → 15 : 9 : 3 : 3
- Hari's share = 15 parts
- Share acquired equally: 15 ÷ 3 = 5 parts each to Chander, Prakash, Govind \[ \text{New Ratio:} \\ \text{Chander: } 9 + 5 = 14 \\ \text{Prakash: } 3 + 5 = 8 \\ \text{Govind: } 3 + 5 = 8 \] 
New ratio = 14 : 8 : 8 Simplify by dividing by  7 : 4 : 4