A and B are partners sharing profit in the ratio of 2:1 respectively A...
Given information:
- A's capital = Rs. 102000
- B's capital = Rs. 73000
- Profit sharing ratio between A and B = 2:1
- C is admitted and given 1/5 share in future profit
- C brings Rs. 14000 as share of goodwill
- C will contribute capital in the new profit sharing ratio
To find: How much capital will be brought by C?
Solution:
Step 1: Calculate the total capital of A and B
- Total capital = A's capital + B's capital
- Total capital = Rs. (102000 + 73000)
- Total capital = Rs. 175000
Step 2: Calculate the profit sharing ratio between A, B, and C
- A and B's ratio = 2:1
- A, B, and C's ratio = 2x : x : y (let's assume C's ratio as y)
- Total ratio = 2x + x + y = 5x + y
- C's share in future profit = 1/5 of total profit
- C's share = (1/5) x (5x + y) = x + (y/5)
Step 3: Calculate the value of x
- A's share = 2/3 of total profit (since A's ratio is 2 out of 3 parts)
- B's share = 1/3 of total profit (since B's ratio is 1 out of 3 parts)
- C's share = x + (y/5) out of total profit
- Total profit = A's share + B's share + C's share
- Total profit = (2/3)x + (1/3)x + (y/5)
- Total profit = (5x + y)/15
- C's share = (1/5) x (5x + y) = x + (y/5)
- Simplifying the above equations, we get:
y = 3x
Step 4: Calculate the total capital after C's admission
- Total capital after C's admission = Total capital + C's share of goodwill
- Total capital after C's admission = Rs. (175000 + 14000)
- Total capital after C's admission = Rs. 189000
Step 5: Calculate the capital contributed by C
- C's ratio = y = 3x
- Total ratio = 2x + x + y = 5x + y
- C's ratio in terms of total ratio = y / (5x + y) = 3x / (5x + 3x) = 3/8
- C's share in total capital after admission = (3/8) x Total capital after admission
- C's share in total capital after admission = (3/8) x 189000
- C's share in total capital after admission = Rs. 70875
Therefore, C will bring Rs. 70875 as capital.
Option C (47250) is not the correct answer.
A and B are partners sharing profit in the ratio of 2:1 respectively A...
Hi there !
The answer is 43,750
Solution :- Combined adjusted capital × reciprocal of new partner share
= (102,000 + 73,000 ) × 1/5 × 5/4 = 43,750
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