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Question
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.
- 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?) - How many more marks were obtained by the student in Mathematics than in Hindi?
- 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
i. Total marks obtained by the student are 540. Hence, 540 marks represent 360º. The central angle for 105 marks has to be calculated.
Central angle for 105 marks = `105/540 xx 360^@ = 70^@`
Hindi is the subject having its central angle as 70º.
Therefore, the student scored 105 marks in Hindi.
ii. Difference between the central angles of Mathematics and Hindi
= 90º − 70º = 20º
Marks for 20º central angle =`20^@/360^@ xx 540 = 30`
There is a difference of 30 marks between the score obtained in Mathematics and Hindi.
Therefore, 30 more marks were obtained by the student in Mathematics than in Hindi.
iii. Marks obtained in Social Science
= Central angle × `"Total mark"/(360°)`
= `65° xx 540/(360°) = 97.5`
Marks obtained in Science
= Central angle × `"Total mark"/(360°)`
= `80° xx 540/(360°) = 120`
So, marks obtained in Social Science and Mathematics
= 97.5 + 135 = 232.5
And marks obtained in Science and Hindi
= 120 + 105 = 225
Thus, (i) and (ii) shows that marks obtained in Mathematics and Social Science is more than that in Science and Hindi.
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