A, B and C are partners in a firm sharing profits in the ratio of 3:2:1. D is admitted into the firm for 1/4th share in profits, which he gets 1/8th from B. The total capital of the firm is agreed upon as Rs. 1,20,000 and D is to bring in cash equivalent to 1/4th of this amount as his capital. The capitals of other partners are also to be adjusted in the ratio of their respective shares in profits. The capitals of A, B and C after all adjustments, are Rs. 40,000, Rs. 35,000 and Rs. 30,000 respectively. Calculate the new capital of A
A, B and C are partners in a firm sharing profits in the ratio of 3:2:1. D is admitted into the firm for 1/4th share in profits, which he gets 1/8th from B. The total capital of the firm is agreed upon as Rs. 1,20,000 and D is to bring in cash equivalent to 1/4th of this amount as his capital. The capitals of other partners are also to be adjusted in the ratio of their respective shares in profits. The capitals of A, B and C after all adjustments, are Rs. 40,000, Rs. 35,000 and Rs. 30,000 respectively. Calculate the new capital of A
Solution
Old ratio: A : B : C = 3/6 : 2/6 : 1/6
D's total share = 1/4
- Gets 1/8 from B
- Remaining = 1/4 - 1/8 = 1/8 to be sacrificed by A and C in their old ratio 3:1
A's sacrifice = 3/4 × 1/8 = 3/32
C's sacrifice = 1/4 × 1/8 = 1/32
Converting all to denominator 96:
| Partner | Old Share | Sacrifice | New Share |
|---|---|---|---|
| A | 48/96 | 9/96 | 39/96 |
| B | 32/96 | 12/96 | 20/96 |
| C | 16/96 | 3/96 | 13/96 |
| D | -- | -- | 24/96 |
New ratio = 39 : 20 : 13 : 24 (total = 96)
Step 2: Calculate New Capitals
Total capital = Rs. 1,20,000
D's capital = 1/4 × 1,20,000 = Rs. 30,000
Remaining for A, B, C = Rs. 90,000, split in ratio 39:20:13 (total 72 parts)
A's new capital = Rs. 48,750
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