Higher Engineering Mathematics, Sixth Edition

532 Higher Engineering Mathematics

correspondingpercentage values in the rows of the table

of percentages. The percentage component bar chart is

shown in Fig. 54.4.

1

10

Percentage relative frequency^20

30

40

50

60

70

80

90

100

23

Year

Key

6-roomed houses

5-roomed houses

4-roomed houses

5-roomed bungalows

4-roomed bungalows

Figure 54.4

Problem 6. The retail price of a product costing

£2 is made up as follows: materials 10p, labour

20p, research and development 40p, overheads

70p, profit 60p. Present these data on a pie diagram.

A circle of any radius is drawn, and the area of the circle

represents the whole, which in this case is £2. The circle

is subdivided into sectors so that the areas of the sectors

are proportional to the parts, i.e. the parts which make

up the total retail price. For the area of a sector to be

proportionaltoa part, the angle at the centre of the circle

must beproportional tothat part.Thewhole,£2or200p,

corresponds to 360◦. Therefore,

10p corresponds to 360×

10

200

degrees, i.e. 18◦

20p corresponds to 360×

20

200

degrees, i.e. 36◦

and so on, giving the angles at the centre of the circle

for the parts of the retail price as: 18◦,36◦,72◦, 126◦

and 108◦, respectively.

The pie diagram is shown in Fig. 54.5.

Problem 7.

(a) Using the data given in Fig. 54.2 only,

calculate the amount of money paid toeach

salesman for travelling expenses, if they are

paid an allowance of 37p per mile.

1088

Ip1.8 8

188

(^728368)
1268
Overheads
Profit
Labour
Research and
development
Materials
Figure 54.5
(b) Using the data presented in Fig. 54.4,
comment on the housing trends over the
three-year period.
(c) Determine the profit made by selling 700
units of the product shown in Fig. 54.5.
(a) By measuring the length of rectangle P the
mileage covered by salesmanPis equivalent to
413miles. Hence salesmanPreceives a travelling
allowance of
£413× 37
100
,i.e.£152. 81
Similarly, for salesmanQ, the miles travelled are
264 and his allowance is
£264× 37
100
,i.e.£97. 68
SalesmanRtravels 597 miles and he receives
£597× 37
100
,i.e.£220. 89
Finally, salesmanSreceives
£143× 37
100
,i.e.£52. 91
(b) An analysis of Fig. 54.4 shows that 5-roomed
bungalows and 5-roomed houses are becoming
more popular, the greatest change in the three
years being a 15% increase in the sales of
5-roomed bungalows.
(c) Since 1.8◦corresponds to 1p and the profit occu-
pies 108◦of the pie diagram, then the profit per
unit is
108 × 1

1. 8
   ,that is, 60p