**1. A survey was made to find the type of music that a certain group of young people liked in a city.**

**Adjoining pie chart shows the findings of this survey. From this pie chart, answer the following:**

(i) If 20 people liked classical music, how many young people were surveyed?

(ii) Which type of music is liked by the maximum number of people?

(iii) If a cassette company were to make 1000 CD’s, how many of each type would they make?

**Solution:**

(i) Let 10% represents 100 people.

So, 20% represents = (100×20)/10 = 200

Hence, 200 people were surveyed.

(ii) Here 40% of the total people surveyed who liked light music and no other form of song. Hence, we can conclude that Light music is liked by the maximum number of people.

(iii)Total CD of classical music = (10 × 1000)/100 = 100

Total CD of semi-classical music = (20 × 1000)/100 = 200

Total CD of light music = (40 × 1000)/100 = 400

Total CD of folk music = (30 × 1000)/100 = 300

**2. A group of 360 people were asked to vote for their favorite season from the three seasons rainy, winter and summer.**

(i) Which season got the most votes?

(ii)Find the central angle of each sector.

(iii) Draw a pie chart to show this information

**Solution:**

(i) According to the given table, Winter season got the most votes.

(ii) According to question:

Central angle of summer season= (90×360)/360= 90^{o}

Central angle of rainy season= (120×360)/360= 120^{o}

Central angle of winter season= (150×360)/360= 150^{o}

(iii)

**3. Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.**

Colours | Number of people |

Blue | 18 |

Green | 9 |

Red | 6 |

Yellow | 3 |

Total | 36 |

**Solution:**

Given, central angle = 360^{o}

Total number of people = 36

Now,

Colours | Number of people | In Fraction | Central angles |

Blue | 18 | 18/36 = ½ | ½ x 360^{o }= 180^{o} |

Green | 9 | 9/36 = ¼ | ¼ x 360^{o }= 90^{o} |

Red | 6 | 6/36 = 1/6 | 1/6 x 360^{o} = 60^{o} |

Yellow | 3 | 3/36 = 1/12 | 1/12 x 360^{o} = 30^{o} |

**4. The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions.**

(i) In which subject did the student score 105 marks?

(Hint: for 540 marks, the central angle = 360°. So, for 105 marks, what is the central angle?)

(ii) How many more marks were obtained by the student in Mathematics than in Hindi?

(iii) Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi. (Hint: Just study the central angles).

**Solution:**

Subject | Central Angle | Marks obtained |

Mathematics | 90^{o} | 90^{o }/360^{o} x 540 = 135 |

Social Science | 65^{o} | 65^{ o} / 360^{ o }x 540 = 97.5 |

Science | 80^{o} | 80^{ o} / 360^{ o} x 540 = 120 |

Hindi | 70^{o} | 70^{ o} / 360^{ o} x 540 = 105 |

English | 55^{o} | 55^{ o} / 360^{ o} x 540 = 82.5 |

**(i)** The student scored 105 marks in Hindi.

**(ii)** Marks obtained in Mathematics by students = 135

Marks obtained in Hindi by students = 105

Difference = 135 – 105 = 30

Hence, Student obtained 30 more marks in Mathematics than in Hindi.

**(iii)** Marks in social science = 97.5

Marks in Mathematics = 225

Marks in Hindi = 105

Now,

The sum of marks in Social Science and Mathematics = 97.5 + 135

= 232.5

The sum of marks in Science and Hindi = 120 + 105 = 225

Hence, the sum of the marks in Social Science and Mathematics is more than that in Science and Hindi.

**5. The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.**

**Solution:**

Language | No. of students | In fraction | Central angle |

Hindi | 40 | 40/72 = 5/9 | 5/9 x 360^{o} = 200^{o} |

English | 12 | 12/72 = 1/6 | 1/6 x 360^{o} = 60^{o} |

Marathi | 9 | 9/72 = 1/8 | 1/8 x 360^{o} = 45^{o} |

Tamil | 7 | 7/72 = 7/72 | 7/72 x 360^{o} = 35^{o} |

Bengali | 4 | 4/72 = 1/18 | 1/18 x 360^{o} = 20^{o} |

Total | 72 |

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