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: 

1. 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?) 
2. How many more marks were obtained by the student in Mathematics than in Hindi? 
3. 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).

Answer 1

Subject	Central Angle	Marks obtained
Mathematics	\(90\degree\)	\(\frac{90\degree}{360\degree}\times540=135\)
Social Science	\(65\degree\)	\(\frac{65\degree}{360\degree}\times540=97.5\)
Science	\(80\degree\)	\(\frac{80\degree}{360\degree}\times540=120\)
Hindi	\(70\degree\)	\(\frac{70\degree}{360\degree}\times540=105\)
English	\(55\degree\)	\(\frac{55\degree}{360\degree}\times540=82.5\)

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

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(ii) Marks obtained in Mathematics = \(135\)
Marks obtained in Hindi = \(105\)
Difference = \(135 – 105 = 30\)
Thus, \(30\) more marks were obtained by the student in Mathematics than in Hindi.

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(iii) The sum of marks in Social Science and Mathematics = \(97.5 + 135 = 232.5\)
The sum of marks in Science and Hindi = \(120 + 105 = 225\)
Yes, the sum of the marks in Social Science and Mathematics is more than that in Science and Hindi.