You decided to join the partnership of august and april. August has a capital of 50,000 while april puts up a capital of 75,000. The three of you decided that your profit and loss ratio would be 1:2:3 for august,april and yourself, and you further agreed to make your capitalization equal to your profit sharing ratio.How much additional capital should april and yourself make to make your capital contributions equal to your profit and loss sharing ratio?
To make the capital contributions equal to the profit and loss sharing ratio, we need to calculate the total capital required based on the given profit sharing ratio of 1:2:3.
Let's calculate the total capital required:
August's profit sharing ratio: 1
Capital contribution by August: $50,000
April's profit sharing ratio: 2
Capital contribution by April: $75,000
Your profit sharing ratio: 3
Capital contribution by you: ?
Using proportions, we can set up the equation:
August's capital / August's profit sharing ratio = Your capital / Your profit sharing ratio
$50,000 / 1 = Your capital / 3
Simplifying the equation:
$50,000 = Your capital / 3
Multiplying both sides by 3 to isolate Your capital:
$50,000 * 3 = Your capital
Your capital = $150,000
Now, to calculate the additional capital required for April and yourself, we can subtract the current capital contributions from the calculated capital required.
Additional capital required for April: $150,000 - $75,000 = $75,000
Additional capital required for you: $150,000 - $0 (assuming you haven't contributed any capital yet) = $150,000
Therefore, April and yourself should each contribute an additional $75,000 and $150,000, respectively, to make the capital contributions equal to the profit and loss sharing ratio.
To determine the additional capital needed for both April and yourself to match the profit and loss sharing ratio, we need to calculate the total capital contribution based on the given ratio.
1. Calculate the total capital contribution:
- August's capital contribution = $50,000
- April's capital contribution = $75,000
- Your capital contribution = unknown (let's call it X)
The profit and loss sharing ratio is given as 1:2:3 for August, April, and yourself, respectively. This means the sum of the ratio is 1 + 2 + 3 = 6.
To determine the total capital, we can set up a proportion:
Capital contribution ratio : Profit and loss sharing ratio = Total capital contribution : Total ratio sum
(1+2+3) : (1:2:3) = (50,000 + 75,000 + X) : 6
2. Solve the proportion:
6 : (1:2:3) = (50,000 + 75,000 + X) : 6
6/6 : 1/6 : 2/6 : 3/6 = (50,000 + 75,000 + X) : 6
1 : 1/6 : 1/3 : 1/2 = (50,000 + 75,000 + X) : 6
Simplifying the ratio on the left side:
6/6 : 1/6 : 2/6 : 3/6 = 1 : 1/6 : 1/3 : 1/2
The ratio on the left side becomes:
1 : 1/6 : 1/3 : 1/2 = (50,000 + 75,000 + X) : 6
Cross-multiplying:
(1 * 6) : (1/6 * 6) : (1/3 * 6) : (1/2 * 6) = (50,000 + 75,000 + X) : 6
6 : 1 : 2 : 3 = (50,000 + 75,000 + X) : 6
Now, equating the left and right sides of the equation:
6 = 50,000 + 75,000 + X
Combine like terms:
6 = 125,000 + X
Subtract 125,000 from both sides:
6 - 125,000 = X
Simplifying:
-124,994 = X
3. Determine the additional capital contributions for April and yourself:
- April's additional capital contribution = -124,994
- Your additional capital contribution = -124,994
Therefore, both April and yourself should contribute an additional capital of -$124,994 to make your capital contributions equal to your profit and loss sharing ratio.