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.