question_answer 1)

                The adjoining pie chart gives the narks 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 \[\text{=36}{{\text{0}}^{o}}\]. 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).

Answer:

                (i) \[\because \] For 540 marks, the central angle \[={{360}^{o}}\] \[\therefore \] For 105 marks, the central angle\[=\frac{{{360}^{\text{o}}}}{{{540}^{\text{o}}}}\times 105={{70}^{\text{o}}}\] Hence, the student scored 105 marks in Hindi. (ii) Marks obtained by the student in Mathematics \[=\frac{{{90}^{\text{o}}}}{{{360}^{\text{o}}}}\times 540=135\]. Marks obtained by the student in Hindi = 105. Hence, the student obtained 135 ? 105 = 30 marks more in Mathematics than in Hindi.                                    (iii) Some of the central angles for Social Science and Mathematics             \[={{65}^{o}}+{{90}^{o}}\] \[={{155}^{o}}\] Sum of the central angles for Science and Hindi. \[={{80}^{o}}+{{70}^{o}}\] \[={{150}^{o}}\] Hence, yes! the sum of the marks obtained in Social Science and Mathematics is more than in Science and Hindi.