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?
(ii) How many more marks were obtained by the students 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

$\begin{array}{ccc}\text{Subject}& \text{Centra Angle}& \text{Marks obtained}\\ \text{Mathematics}& {90}^{\circ }& \frac{{90}^{\circ }}{{360}^{\circ }}\times 540=135\\ \text{Social Science}& {65}^{\circ }& \frac{{65}^{\circ }}{{360}^{\circ }}\times 540=97.5\\ \text{Science}& {80}^{\circ }& \frac{{80}^{\circ }}{{360}^{\circ }}\times 540=120\\ \text{Hindi}& {70}^{\circ }& \frac{{70}^{\circ }}{{360}^{\circ }}\times 540=105\\ \text{English}& {55}^{\circ }& \frac{{55}^{\circ }}{{360}^{\circ }}\times 540=82.5\end{array}$

(i) The student scored 105 marks in Hindi.

(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.

(iii) The central angle for maths is ${90}^{\circ }$ and central angle for Social science is ${65}^{\circ }$
$\therefore$ Their sum is ${90}^{\circ }+{65}^{\circ }={155}^{\circ }$
The central angle for Science is ${80}^{\circ }$ and central angle for Hindi is ${70}^{\circ }$
$\therefore$Their sum is ${80}^{\circ }+{70}^{\circ }={150}^{\circ }$
Yes, the sum of the marks in Social Science and Mathematics is more than that in Science and Hindi.