A, B, C and D are partners. A and B share 2/3rd of profits equally and C and D share remainingprofits in the ratio of 3:2. Find the profit sharing ratio of A.

1. Break Down the Problem

• A and B share 2/3 of the total profits equally.
• C and D share the remaining profits, which is 1/3 of the total profits, in the ratio of 3:2.

2. Relevant Concepts

• The profit sharing ratio needs to be calculated for each partner based on their contributions to the total profit:
  • A and B’s share = $\frac{2}{3}$
  • C and D’s share = $\frac{1}{3}$ (remaining profits)

3. Analysis and Detail

• A and B's Share:

  • Since A and B share the profits equally, each will get: $\text{Share of A} = \text{Share of B} = \frac{1}{2} \times \frac{2}{3} = \frac{1}{3}$

• C and D's Share:

  • The total profit left for C and D is $\frac{1}{3}$. This will be divided in the ratio of 3:2.
  • Total parts = $3 + 2 = 5$
  • Each part value for C and D: $\text{Value of each part} = \frac{\frac{1}{3}}{5} = \frac{1}{15}$
  • C’s share: $\text{Share of C} = 3 \times \frac{1}{15} = \frac{3}{15} = \frac{1}{5}$
  • D’s share: $\text{Share of D} = 2 \times \frac{1}{15} = \frac{2}{15}$

4. Verify and Summarize

• The total shares:
  • A's share = $\frac{1}{3}$
  • B's share = $\frac{1}{3}$
  • C's share = $\frac{1}{5}$
  • D's share = $\frac{2}{15}$

Final Answer

The profit sharing ratio for A is $\frac{1}{3}$.