Question

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.
(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%.