Question

A survey was conducted to know the number of cars, buses and motorcycles that pass a

junction. The result is depicted in the following pie-chart. If there were 150 buses in the

survey then answer the following questions:

(i) What percentage of vehicles passing by the junction

were cars?

(ii) Calculate the total number of vehicles in the survey?

(iii) Find the number of motorcycles included in the survey?​

Answer 1

Answer:

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Step-by-step explanation:

a) To convert the angle of a sector into a percentage, we use the formula:

Percentage = angle of sector/360 degree*100

Percentage of cars = 120/360*100 = 33.3%

b) Let x be the total number of vehicles

30/360*x = 150

=> x = 150*360/30

=> x = 1800

The total number of vehicles is 1,800

c) Let x be the total number of motorcycle

210/360*x = 150

=> x = 150*360/210

=> x = 257.14  i.e. 257

The total number of vehicles is 257

Answer 2

According to give details in above question.

We have to find the following question from above survey .

Step-by-step explanation:

Given ,

Total angle of sector of pie chart= 360°

Angle of sector of Motorcycle= 210°

Angle of sector of Buses=30°

Angle of sector of Cars= 120°

Solution 1:

Percentage of vehicles passing by the junction were cars:

$Percentage= \frac{given \: }{total} \times 100\%$

Given= 120°

Total= 360°

Put the values ,we get

$Percentage \: of \: cars= \frac{120}{360} \times 100\%$

$Percentage \: of \: cars= \frac{1}{3} \times 100$

Multiply 1 by 100 in numerator,

$Percentage \: of \: cars= \frac{100}{3}$

Divide the terms

$Percentage \: of \: cars=33.3\%$

Solution 2:

Total number of vehicles in the survey.

Let number be x

The equation becomes ,

$\frac{30}{360} of \: x = 150$

change of into multiply

$\frac{30}{360} \times \: x = 150$

Divide the terms

$\frac{1}{12} \times \: x = 150$

$\frac{x}{12} = 150$

Cross- multiply ther terms ,

$x = 150 \times 12$

$x = 1800 \: vehicles$

Solution 3:

Let y be the Number of Motorcycle:

$y = \frac{210}{360} \times 1800$

Divide fraction by 30

$y = \frac{210 \div 30}{360 \div 30} \times 1800$

$y = \frac{7}{12} \times 1800$

Multiply 7 by 1800

$y = \frac{12600}{12}$

or,

$y = 1050$

Hence ,

1. 33.3%

2.x= 1800 vehicles

3. y= 1050 Motorcycle

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