Sandeep and Navdeep are partners in a firm sharing profits in 5:3 ratio. They admit C into the firm and the new profit sharing ratio was agreed at 4:2:1. Calculate the sacrificing ratio?
3:5
Explanation
The textbook context defines Sacrificing Ratio as the ratio in which old partners agree to sacrifice their share of profit in favour of the incoming partner. The formula provided is Old Share of Profit – New Share of Profit. For this specific question, the context explicitly provides the answer as 3:5. By calculating the difference between the old shares (5/8 and 3/8) and the new shares (4/7 and 2/7), we derive the fraction of sacrifice for each partner, which simplifies to the ratio 3:5.
Solution Steps
Step 1: Calculate Old Profit Shares. Old Ratio (Sandeep : Navdeep) = 5:3 Sandeep's Old Share = 5/8 Navdeep's Old Share = 3/8
Step 2: Calculate New Profit Shares. New Ratio (Sandeep : Navdeep : C) = 4:2:1 Total Share = 4 + 2 + 1 = 7 Sandeep's New Share = 4/7 Navdeep's New Share = 2/7
Step 3: Calculate Sacrifice for each partner. Sacrifice = Old Share – New Share Sandeep's Sacrifice = 5/8 - 4/7 = (35 - 32)/56 = 3/56 Navdeep's Sacrifice = 3/8 - 2/7 = (21 - 16)/56 = 5/56
Step 4: Determine Sacrificing Ratio. Sacrificing Ratio (Sandeep : Navdeep) = 3/56 : 5/56 Sacrificing Ratio = 3:5