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.
(i) In which subject did the student score $105$ marks? 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.

Answer 1

(i)

Total marks obtained $=540$
${540}^{\circ }$ represents ${360}^{\circ }$
$\therefore$ The central angle for $105$ marks:
$=\frac{105}{540}\times {360}^{\circ }$ $={70}^{\circ }$
Hindi's central angle is ${70}^{\circ }$
$\therefore$ Student scored $105$ marks in Hindi

(ii)

Difference between central angles of Maths and Hindi
$\Rightarrow {90}^o-{70}^o\Rightarrow {20}^o$
Marks for ${20}^{\circ }$ central angles $=\frac{20}{360}\times {540}^{\circ }={30}^{\circ }$
$\therefore 30$ more marks were obtained by student in maths than in hindi

(iii)

Sum of central angles of social science and maths
$={65}^{\circ }+{90}^{\circ }={155}^{\circ }$
Sum of central angles of Science and Hindi $={80}^{\circ }+{70}^{\circ }={150}^{\circ }$
Sum of central angles for social Science and Mathematics > Science and Hindi.