question_answer

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.

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

(Hint: for 540 marks, the central angle = \[360{}^\circ ).\]

So, for 105 marks what is the central angle?

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

(c) 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:

Subject	Centre angle	Marks obtained
Hindi	\[70{}^\circ \]	\[\frac{70}{360}\times 540=105\]
English	\[55{}^\circ \]	\[\frac{55}{360}\times 540=82.5\]
Mathematics	\[90{}^\circ \]	\[\frac{90}{360}\times 540=135\]
Social Science	\[65{}^\circ \]	\[\frac{65}{360}\times 540=97.5\]
Science	\[80{}^\circ \]	\[\frac{80}{360}\times 540=120\]

(a) In Hindi student score 105 marks.

(b) Marks scored in Mathematics = 135

& Marks scored in Hindi = 105

\[~\because 135105=30\]

\[\therefore \] 30 more marks were obtained by the students in Mathematics than in Hindi.

(c) Yes, Sum of marks obtained in Social Science & Mathematics \[=97.5+135=\text{ }232.5\]

Sum of marks obtained in Science & Hindi \[=120+105=225\]

Hence, the sum of the marks obtained in Social Science & Mathematics is more than that in Science & Hindi