Singh, Gupta and Khan are partners in a firm sharing profits in 3:2:3 ratio. They admitted Jain as a new partner. Singh surrendered 1/3 of his share in favour of Jain: Gupta surrendered 1/4 of his share in favour of Jain and Khan surrendered 1/5 in favour of Jain. Calculate new profit sharing ratio?
New Profit Sharing Ratio of Singh, Gupta, Khan and Jain is 20:15:24:21.
Explanation
The calculation follows the method where the new partner's share is the sum of the shares surrendered by the old partners. The new share of each old partner is calculated by deducting the surrendered share from their old share. This logic is consistent with the illustrations provided in the context, specifically Illustration 3 and 4.
Solution Steps
Step 1: Calculate Old Profit Sharing Ratio. Singh : Gupta : Khan = 3 : 2 : 3. Let total profit = 1. Singh's Share = 3/8 Gupta's Share = 2/8 Khan's Share = 3/8
Step 2: Calculate Share Surrendered in favour of Jain. Singn surrenders 1/3 of his share = 1/3 of 3/8 = 3/24 = 1/8. Gupta surrenders 1/4 of his share = 1/4 of 2/8 = 2/32 = 1/16. Khan surrenders 1/5 of his share = 1/5 of 3/8 = 3/40.
Step 3: Calculate New Shares of Old Partners. Singh's New Share = Old Share - Surrendered Share = 3/8 - 1/8 = 2/8. Gupta's New Share = Old Share - Surrendered Share = 2/8 - 1/16 = 4/16 - 1/16 = 3/16. Khan's New Share = Old Share - Surrendered Share = 3/8 - 3/40 = 15/40 - 3/40 = 12/40.
Step 4: Calculate Jain's Share. Jain's Share = Sum of Surrendered Shares = 1/8 + 1/16 + 3/40 Taking LCM of 8, 16, 40 = 80. = 10/80 + 5/80 + 6/80 = 21/80.
Step 5: Determine New Profit Sharing Ratio. Convert all shares to a common denominator (80): Singh = 2/8 = 20/80 Gupta = 3/16 = 15/80 Khan = 12/40 = 24/80 Jain = 21/80 New Ratio (Singh : Gupta : Khan : Jain) = 20 : 15 : 24 : 21.