A salesman received a basic salary of sh.50000 a year and a commission of 6% on the value of goods sold and a car allowance of sh.2.50 per km.

Question

(a) find the total amount he received in a year in which he sells goods worth sh.625000 and travels a distance of 10000km
(b) the next year he travels 12000km and receives a total of sh.134000
(I) calculate the value of goods sold
(Ii) calculate the percentage increase in the value of the goods sold

Answer 1

To solve the problem, let’s break it down step by step.

Part (a)

1. Basic Salary: sh. 50,000
2. Commission Rate: 6%
3. Goods Sold: sh. 625,000
4. Car Allowance Rate: sh. 2.50 per km
5. Distance Travelled: 10,000 km

Step 1: Calculate the Commission \[ \text{Commission} = \text{Goods Sold} \times \text{Commission Rate} \] \[ \text{Commission} = 625,000 \times 0.06 = 37,500 \]

Step 2: Calculate the Car Allowance \[ \text{Car Allowance} = \text{Distance} \times \text{Car Allowance Rate} \] \[ \text{Car Allowance} = 10,000 \times 2.50 = 25,000 \]

Step 3: Calculate Total Amount for the Year \[ \text{Total Amount} = \text{Basic Salary} + \text{Commission} + \text{Car Allowance} \] \[ \text{Total Amount} = 50,000 + 37,500 + 25,000 = 112,500 \]

Answer for (a): The total amount he received in the year is sh. 112,500.

Part (b)

1. Total Amount Received the Next Year: sh. 134,000
2. Distance Travelled: 12,000 km

(i) Calculate the Value of Goods Sold:

1. Total Car Allowance for Next Year: \[ \text{Car Allowance} = \text{Distance} \times \text{Car Allowance Rate} \] \[ \text{Car Allowance} = 12,000 \times 2.50 = 30,000 \]

2. Find Total Income Excluding Commission: \[ \text{Income from Salary and Car Allowance} = \text{Total Amount} - \text{Car Allowance} \] \[ \text{Income from Salary and Car Allowance} = 134,000 - 30,000 = 104,000 \]

3. Calculate the Commission from Salary and Total Income: Using the basic salary of sh. 50,000: \[ \text{Commission} = \text{Income from Salary and Car Allowance} - \text{Basic Salary} \] \[ \text{Commission} = 104,000 - 50,000 = 54,000 \]

4. Calculate Value of Goods Sold \[ \text{Commission} = \text{Value of Goods Sold} \times \text{Commission Rate} \] \[ 54,000 = \text{Value of Goods Sold} \times 0.06 \] \[ \text{Value of Goods Sold} = \frac{54,000}{0.06} = 900,000 \]

Answer for (i): The value of goods sold in the next year is sh. 900,000.

(ii) Calculate the Percentage Increase in the Value of Goods Sold:

1. Previous Year Goods Sold: sh. 625,000
2. Next Year Goods Sold: sh. 900,000

Calculate the Increase: \[ \text{Increase} = \text{Next Year Goods Sold} - \text{Previous Year Goods Sold} \] \[ \text{Increase} = 900,000 - 625,000 = 275,000 \]

Calculate the Percentage Increase: \[ \text{Percentage Increase} = \left( \frac{\text{Increase}}{\text{Previous Year Goods Sold}} \times 100 \right) \] \[ \text{Percentage Increase} = \left( \frac{275,000}{625,000} \times 100 \right) = 44% \]

Answer for (ii): The percentage increase in the value of the goods sold is 44%.