Question

The sales of a salesman in a week are represented in the pie diagram below. Study the diagram and answer the following questions:
If the total sale due to salesman A is Rs 18,000,
(a) find the sales of each salesman
(b) find the salesman with the highest sale
(c) find the difference between the highest sale and the lowest sale
(d) find the total sale

Fig 6.26

Answer 1

$$\begin{gathered} \left(\mathrm{a}\right)\mathrm{Total}\mathrm{sale}\text{s}\text{of}\mathrm{salesman}\mathrm{A}=\mathrm{Rs}18,000 \\ \mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{total}\mathrm{sale}\text{s}\text{of}\mathrm{salesman}\mathrm{A}=90° \\ \mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{total}\mathrm{sale}\text{s}\text{of}\mathrm{salesman}\mathrm{A}=\frac{\mathrm{Total}\mathrm{sale}\text{s}\text{of}\mathrm{salesman}\mathrm{A}}{\mathrm{Total}\mathrm{sale}s}\times 360° \\ 90°=\frac{18000}{\mathrm{Total}\mathrm{sale}\text{s}}\times 360° \\ \therefore \mathrm{Total}\mathrm{sale}\text{s}=\frac{18000\times 360}{90} \\ =\mathrm{Rs}72,000 \end{gathered}$$

$$\begin{gathered} \mathrm{Now},\mathrm{we}\mathrm{have}\mathrm{to}\mathrm{calculate}\mathrm{the}\mathrm{sales}\mathrm{of}\mathrm{each}\mathrm{salesman}: \\ \mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{total}\mathrm{sales}\text{of}\mathrm{salesman}\mathrm{B}=\frac{\mathrm{Total}\mathrm{sale}s\text{of}\mathrm{salesman}\mathrm{B}}{\mathrm{Total}\mathrm{sale}\text{s}}\times 360° \\ \Rightarrow 120°=\frac{\mathrm{Total}\mathrm{sale}s\text{of}\mathrm{salesman}\mathrm{B}}{72000}\times 360° \\ \therefore \mathrm{Total}\mathrm{sale}\text{s}\text{of}\mathrm{salesman}\mathrm{B}=\frac{120\times 72000}{360}=\mathrm{Rs}24,000 \end{gathered}$$

$$\begin{gathered} \mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{total}\mathrm{sale}\text{s}\text{of}\mathrm{salesman}\mathrm{C}=\frac{\mathrm{Total}\mathrm{sale}\text{s}\text{of}\mathrm{salesman}C}{\mathrm{Total}\mathrm{sale}\text{s}}\times 360° \\ 80°=\frac{\mathrm{Total}\mathrm{sale}s\text{of}\mathrm{salesman}\mathrm{C}}{72000}\times 360° \\ \therefore \mathrm{Total}\mathrm{sale}\text{s}\text{o}\text{f}\mathrm{salesman}\mathrm{C}=\frac{80\times 72000}{360}=\mathrm{Rs}16,000 \end{gathered}$$

$$\begin{gathered} \mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{total}\mathrm{sale}s\text{of}\mathrm{salesman}\mathrm{D}=\frac{\mathrm{Total}\mathrm{sale}s\text{of}\mathrm{salesman}\mathrm{D}}{\mathrm{Total}\mathrm{sale}\text{s}}\times 360° \\ 70°=\frac{\mathrm{Total}\mathrm{sale}s\text{of}\mathrm{salesman}\mathrm{D}}{72000}\times 360° \\ \therefore \mathrm{Total}\text{sales}\text{of}\mathrm{salesman}\mathrm{D}=\frac{70\times 72000}{360}=\mathrm{Rs}14,000 \end{gathered}$$


The table given below shows the sales of each salesman.

A	B	C	D
Rs 18,000	Rs 24,000	Rs 16,000	Rs 14,000

(b) Salesman B had the highest sales, i.e. Rs 24,000.
(c) Highest sales = Rs 24,000
Lowest sales = Rs 14,000
Difference between the highest sales and the lowest sales = Rs (24000-14000) = Rs 10,000.

(d) As calculated in part (a), total values of sales is Rs 72,000.