(i) Given, 20 people liked classical music. From the pie chart, we can see that classical music is liked by 10% of young people in the city. Let the total number of people in the city = x
Given, 10% of x = 20
(10/100) * x = 20
x = (20 * 100) / 10 = 200
So, 200 young people were surveyed.
(ii) Since light music occupies a maximum percentage (40%) in the pie chart, it is liked by the maximum number of people.
(iii) If a cassette company were to make 1000 CD’s, they would make
Classical music CDs = 10% of 1000
= (10 / 100) * 1000
= 100 CDs
Semi Classical music CDs = 20% of 1000
= (20 / 100) * 1000
= 200 CDs
Folk music CDs = 30% of 1000
= (30 / 100) * 1000
= 300 CDs
Light music CDs = 40% of 1000
= (40 / 100) * 1000
= 400 CDs
(i) Winter season got the most votes (150).
(ii) Find the proportion and percentage of each sector to calculate the central angle of each sector.
Total votes = 90 + 120 + 150 = 360
Proportion of summer season = 90 / 360 = 1 / 4, Percentage = (1 / 4) * 100 = 25%
Proportion of rainy season = 120 / 360 = 1 / 3, Percentage = (1 / 3) * 100 = 33.334%
Proportion of winter season = 150 / 360 = 5 / 12, Percentage = (5 / 12) * 100 = 41.667%
Now, the central angle of each sector is,
Summer season = (25 / 100) * 360° = 90°
Rainy season = (33.334 / 100) * 360° = 120°
Winter season = (41.667 / 100) * 360° = 150°
Find the proportion and percentage of each sector to calculate the central angle of each sector.
Total number of people = 18 + 9 + 6 + 3 = 36
Proportion of Blue = 18 / 36 = 1 / 2, Percentage = (1 / 2) * 100 = 50%
Proportion of Green = 9 / 36 = 1 / 4, Percentage = (1 / 4) * 100 = 25%
Proportion of Red = 6 / 36 = 1 / 6, Percentage = (1 / 6) * 100 = 16.667%
Proportion of Yellow = 3 / 36 = 1 / 12, Percentage = (1 / 12) * 100 = 8.334%
Now, the central angle of each sector is,
Blue = (50 / 100) * 360° = 180°
Green= (41.667 / 100) * 360° = 90°
Red = (16.667 / 100) * 360° = 60°
Yellow = (8.334 / 100) * 360° = 30°
(i) Given, total marks obtained by the students were 540, So,
For 540 marks, the central angle = 360°
For 1 mark, the central angle = (360 / 540)°
For 105 marks, the central angle = ((360 / 540) * 105)°
= 70°
From the given pie chart, 70° corresponds to Hindi language. Therefore, the student score 105 marks in Hindi.
(ii) In mathematics, marks scored = (90 / 360) * 540
= 135 marks
In hindi, marks scored = (70 / 360) * 540
= 105 marks
Therefore, the student scored (135 - 105) = 30 marks more in Mathematics than in Hindi.
(iii) In mathematics, marks scored = 135 marks
In hindi, marks scored = 105 marks
In social science, marks scored = (65 / 360) * 540
= 97.5 marks
In science, marks scored = (80 / 360) * 540
= 120 marks
Marks in social science + mathematics = 97.5 + 135 = 232.5
Marks in science + hindi = 120 + 105 = 225
232.5 > 225
Yes, the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.
Alternative way:
Central angle of social science + mathematics = 65° + 90° = 155°
Central angle of science + hindi = 80° + 70° = 150°
155° > 150°
Yes, the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.
Find the proportion and percentage of each sector to calculate the central angle of each sector.
Total number of students = 72
Proportion of Hindi = 40 / 72 = 5 / 9, Percentage = (5 / 9) * 100 = 55.556%
Proportion of English = 12 / 72 = 1 / 6, Percentage = (1 / 6) * 100 = 16.667%
Proportion of Marathi = 9 / 72 = 1 / 8, Percentage = (1 / 8) * 100 = 12.5%
Proportion of Tamil = 7 / 72 = 7 / 72, Percentage = (7 / 72) * 100 = 9.723%
Proportion of Bengali = 4 / 72 = 1 / 18, Percentage = (1 / 18) * 100 = 5.556%
Now, the central angle of each sector is,
Hindi = (55.556 / 100) * 360° = 200°
English = (16.667 / 100) * 360° = 60°
Marathi = (12.5 / 100) * 360° = 45°
Tamil = (9.723 / 100) * 360° = 35°
Bengali = (5.556 / 100) * 360° = 20°