Observe the adjacent pie diagram. It shows the percentages of number of vehicles passing a signal in a town between 8 am and 10 am

(1) Find the central angle for each type of vehicle.

(2) If the number of two-wheelers is 1200, find the number of all vehicles.

(1) To find central angle for cars:

Given that, percentage of cars passing a signal in a town = 30%

⇒ Number of cars = 30

& Total number of vehicles = 100

Central angle for cars is given by,

⇒

⇒ Central angle for cars = 108°

Thus, central angle for cars is 108°.

To find central angle for tempos:

Given that, percentage of tempos passing a signal in a town = 12%

⇒ Number of tempos = 12

& Total number of vehicles = 100

Central angle for tempos is given by,

⇒

⇒ Central angle for tempos = 43.2°

By approximating, we get

Central angle for tempos = 43°

Thus, central angle for tempos is 43.2°.

To find central angle for buses:

Given that, percentage of buses passing a signal in a town = 8%

⇒ Number of buses = 8

& Total number of vehicles = 100

Central angle for buses is given by,

⇒

⇒ Central angle for buses = 28.8°

By approximating, we get

Central angle for buses = 29°

Thus, central angle for buses is 29°.

To find central angle for auto-rikshaws:

Given that, percentage of auto-rikshaws passing a signal in a town = 10%

⇒ Number of auto-rikshaws = 10

& Total number of vehicles = 100

Central angle for auto-rikshaws is given by,

⇒

⇒ Central angle for auto-rikshaws = 36°

Thus, central angle for auto-rikshaws is 36°.

To find central angle for two-wheelers:

Given that, percentage of two-wheelers passing a signal in a town = 40%

⇒ Number of two-wheelers = 40

& Total number of vehicles = 100

Central angle for two-wheelers is given by,

⇒

⇒ Central angle for two-wheelers = 144°

Thus, central angle for two-wheelers is 144°.

Check: Add all central angles for vehicles (cars + tempos + buses + auto-rikshaws + two-wheelers) = 108° + 43° + 29° + 36° + 144° = 360°

Hence, it’s correct.

(2). Given: Number of two-vehicles = 1200

And central angle for two-vehicles = 144° (as found in part (1))

Then,

⇒

⇒

⇒ Total number of vehicles = 3000

Thus, there are total 3000 vehicles in all.