Question

The following pie diagram represents expenditure on different items in constructing a building. Answer the following questions.

(a) Find the expenditure on each of the items if the total construction cost is Rs 5,40,000.
(b) Which is the item that incurred the maximum expenditure ?
(c) Which is the item that incurred the minimum expenditure?

Fig 6.6

Answer 1

(a) Central angle for expenditure on cement =75^o
$$\begin{gathered} \mathrm{Central}\mathrm{angle}\mathrm{for}\mathrm{expenditure}\mathrm{on}\mathrm{cement}=\frac{\mathrm{Expenditure}\mathrm{on}\mathrm{cement}}{\mathrm{Total}\mathrm{expenditure}}\times 360° \\ \therefore 75°=\frac{\mathrm{Expenditure}\mathrm{on}\mathrm{cement}}{540000}\times 360° \\ \therefore \mathrm{Expenditure}\mathrm{on}\mathrm{cement}=\mathrm{Rs}1,12,500 \end{gathered}$$


$$\begin{gathered} \mathrm{Central}\mathrm{angle}\mathrm{for}\mathrm{the}\mathrm{expenditure}\mathrm{on}\mathrm{bricks}=50° \\ \mathrm{Central}\mathrm{angle}\mathrm{for}\mathrm{the}\mathrm{expenditure}\mathrm{on}\mathrm{bricks}=\frac{\mathrm{Expenditure}\mathrm{on}\mathrm{bricks}}{\mathrm{Total}\mathrm{expenditure}}\times 360° \\ \therefore 50°=\frac{\mathrm{Expenditure}\mathrm{on}\mathrm{bricks}}{540000}\times 360° \\ \therefore \mathrm{Expenditure}\mathrm{on}\mathrm{bricks}=\mathrm{Rs}75,000 \end{gathered}$$


$$\begin{gathered} \mathrm{Central}\mathrm{angle}\mathrm{for}\mathrm{the}\mathrm{expenditure}\mathrm{on}\mathrm{labour}=100° \\ \mathrm{Central}\mathrm{angle}\mathrm{for}\mathrm{the}\mathrm{expenditure}\mathrm{on}\mathrm{labour}=\frac{\mathrm{Expenditure}\mathrm{on}\mathrm{labour}}{\mathrm{Total}\mathrm{expenditure}}\times 360° \\ \therefore 100°=\frac{\mathrm{Expenditure}\mathrm{on}\mathrm{labour}}{540000}\times 360° \\ \therefore \mathrm{Expenditure}\mathrm{on}\mathrm{labour}=\mathrm{Rs}1,50,000 \end{gathered}$$


$$\begin{gathered} \mathrm{Central}\mathrm{angle}\mathrm{for}\mathrm{the}\mathrm{expenditure}\mathrm{on}\text{t}\mathrm{imber}=90° \\ \mathrm{Central}\mathrm{angle}\mathrm{for}\mathrm{the}\mathrm{expenditure}\mathrm{on}\text{t}\mathrm{imber}=\frac{\mathrm{Expenditure}\mathrm{on}\text{t}\mathrm{imber}}{\mathrm{Total}\mathrm{expenditure}}\times 360° \\ \therefore 90°=\frac{\mathrm{Expenditure}\mathrm{on}\text{t}\mathrm{imber}}{540000}\times 360° \\ \therefore \mathrm{Expenditure}\mathrm{on}\text{timber}=\mathrm{Rs}1,35,000 \end{gathered}$$


$$\begin{gathered} \mathrm{Central}\mathrm{angle}\mathrm{for}\mathrm{the}\mathrm{expenditure}\mathrm{on}\text{s}\mathrm{teel}=45° \\ \mathrm{Central}\mathrm{angle}\mathrm{for}\mathrm{the}\mathrm{expenditure}\mathrm{on}\text{s}\mathrm{teel}=\frac{\mathrm{Expenditure}\mathrm{on}\text{s}\mathrm{teel}}{\mathrm{Total}\mathrm{expenditure}}\times 360° \\ \therefore 45°=\frac{\mathrm{Expenditure}\mathrm{on}\text{s}\mathrm{teel}}{540000}\times 360° \\ \therefore \mathrm{Expenditure}\mathrm{on}\text{s}\mathrm{teel}=\mathrm{Rs}67,500 \end{gathered}$$

Cement	Bricks	Labour	Timber	Steel
Rs 1,12,500	Rs 75,000	Rs 1,50,000	Rs 1,35,000	Rs 67,500

(b) Labour incurred the maximum expenditure, i.e Rs 1,50,000.

(c) Steel incurred the minimum expenditure, i.e Rs 67,500.