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A and B are partners in a firm sharing profits and losses in the ratio of 5:3. They decided to admit C as a new partner in the firm with 1/5 share in profits, this share is contributed by them in the ratio of 2:1. Calculate he new ratio of the partners?
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A and B are partners in a firm sharing profits and losses in the ratio...
Solution:

Given:

  • Ratio of profits and losses shared by A and B = 5:3

  • They decided to admit C as a new partner with 1/5 share in profits

  • This share is contributed by A and B in the ratio of 2:1



Step 1: Calculate the current share of profits for A and B

  • Let the total profit be x

  • A's share of profit = 5/8 * x

  • B's share of profit = 3/8 * x



Step 2: Calculate the new share of profits for A, B, and C

  • Let C's share of profit be y

  • Then, the total profit after C's admission = x + y

  • According to the given condition, A and B contribute in the ratio of 2:1 to C's share of profit

  • So, A's contribution = 2/3 * y and B's contribution = 1/3 * y

  • Therefore, the new share of profit for A, B, and C is:

  • A = 5/8 * x + 2/3 * y

  • B = 3/8 * x + 1/3 * y

  • C = 1/5 * (x + y)



Step 3: Simplify the above expressions

  • Multiply A's expression by 24/24 and B's expression by 24/24 to get a common denominator:

  • A = 15x/24 + 16y/24

  • B = 9x/24 + 8y/24

  • Combine the expressions for A and B to get the total profit:

  • Total profit = A + B + C = 5x/8 + 2y/3 + 3x/8 + y/3 + (x + y)/5

  • Simplify and multiply by 120/120 to get a common denominator:

  • Total profit = 75x/120 + 80y/120 + 45x/120 + 40y/120 + 24x/120 + 24y/120

  • Total profit = 144x/120 + 144y/120

  • Total profit = 6x/5 + 6y/5

  • Substitute this value in the expressions for A, B, and C:

  • A = 15x/24 + 16y/24 = 5x/8 + 2y/3

  • B = 9x/24 + 8y/24 = 3x/8 + y/3

  • C = 1/5 * (x + y) = 24x/120 + 24y/120



Step 4: Express the new ratio of profits and losses

  • New ratio of profits and losses = A
Community Answer
A and B are partners in a firm sharing profits and losses in the ratio...
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A and B are partners in a firm sharing profits and losses in the ratio of 5:3. They decided to admit C as a new partner in the firm with 1/5 share in profits, this share is contributed by them in the ratio of 2:1. Calculate he new ratio of the partners?
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