Question

Atienoand kamau started a bussinessby contributing25000 and20000respectivelyat the end of the year they realized a profit of 81000 .the profit was allocated to development,dividence, reserve in the ratio of 4:5:6 respectively .Thedividence were then shared in the ratio of their contribution calculate the dividence paid to atieno

Answer 1

To calculate the dividend paid to Atieno, we will follow these steps:

1. **Calculate the total ratio for profit allocation** and determine how much of the profit is allocated to each category (development, dividend, reserve).

2. **Calculate the amounts allocated** to each category based on the total profit.

3. **Calculate the dividends** to be shared between Atieno and Kamau based on their contributions.

### Step 1: Profit Allocation Ratio

The profit was allocated to development, dividend, and reserve in the ratio of 4:5:6.

First, we find the total parts of the ratio:
\[ 4 + 5 + 6 = 15 \]

### Step 2: Calculate Amounts for Each Category

Now we calculate how much of the total profit of 81,000 is allocated to each category.

1. **Development**:
\[
\text{Development} = \left( \frac{4}{15} \right) \times 81,000 = 21,600
\]

2. **Dividend**:
\[
\text{Dividend} = \left( \frac{5}{15} \right) \times 81,000 = 27,000
\]

3. **Reserve**:
\[
\text{Reserve} = \left( \frac{6}{15} \right) \times 81,000 = 32,400
\]

### Step 3: Calculate Dividends Shared Based on Contributions

The dividends of 27,000 need to be shared between Atieno and Kamau based on their contributions.

- Atieno's contribution: 25,000
- Kamau's contribution: 20,000

Total contribution:
\[ 25,000 + 20,000 = 45,000 \]

Now, we find the share of the dividend each person receives:

1. **Atieno's share of the dividend**:
\[
\text{Atieno's share} = \left( \frac{25,000}{45,000} \right) \times 27,000
\]

Calculating it:
\[
\text{Atieno's share} = \left( \frac{25}{45} \right) \times 27,000 = \left( \frac{5}{9} \right) \times 27,000 = 15,000
\]

### Final Answer

The dividend paid to Atieno is **15,000**.