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).

 

(i) For 540 marks, the central angle = 360°
For 105 marks the central angle = $\frac{360}{540}\times 105$ = 70° 

Hence, the corresponding subject in which the student score 105 marks is Hindi.

(ii) Marks obtained in Mathematics = $\frac{90}{360}\times 540$ = 135

Marks obtained in Hindi= 105

Marks obtained in Mathematics more than Hindi = 135 – 105 = 30

(iii) Central angle of Social Science + Mathematics = 65° + 90° = 155°

Central angle of Science + Hindi = 80° + 70° = 150°

Since, the Central angle of Social Science + Mathematics is more than Central angle of Science + Hindi

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