Question

What is the percentage of marks obtained by the students in the periodical exams of August, $01$ and October, $01$ taken together?

$\begin{align}
  & (a)73.25\% \\
 & (b)75.5\% \\
 & (c)77\% \\
 & (d)78.75\% \\
\end{align}$

Answer 1

Hint: In this question, we are given a line graph in which we are given marks obtained by students in six periodicals held in every two months during the year in session $2001-2002$. We have to calculate the percentage of marks obtained by the students in periodical exams of August, $01$ and October, $01$ taken together. For this, we will calculate the marks obtained by students in August, $01$ and October, $01$ from the graph and add them to get the total marks obtained. Since the formula for calculating the percentage is given by \[\left( \dfrac{marks~obtained}{total~marks}\times 100 \right)\%\], therefore we require total marks also. We are given in the graph that the maximum total marks in each periodical exam is $500$. So we will calculate total marks of both months and put them in the formula to get the required result.

Complete step by step answer:
Here, we are given a line graph in which we are given marks obtained by students in six periodicals held every two months during the year in session $2001-2002$. From the graph, we can analyze that in the month of April, $01$, students obtained $360$ marks. In the month June,$01$, students obtained $365$ marks. In the month August, $01$, students obtained $370$ marks. In the month October, $01$, students obtained $385$ marks. In December, $01$, students obtained $400$ marks and in the month February, $01$, students obtained $405$ marks.
Since, we need to find the percentage of marks obtained by the students in periodical exams of August, $01$ and October, $01$ taken together, so we will use the formula –
Percentage of marks $=\left( \dfrac{marks~obtained}{total~marks}\times 100 \right)\%$
For August, $01$, marks are $370$ and for October, $01$, marks are $385$. For calculating marks together, total marks obtained becomes $370+385=755$. Also, we are given that total marks obtained in each periodical exam is $500$. Hence, total marks for two months become $500+500=1000$.
Putting both values in formula, we get –
$Percentage=\left( \dfrac{755}{1000}\times 100 \right)\%=75.5\%$

Hence, the percentage of marks obtained by students in periodical exams of August, $01$ and October, $01$ taken together will be $75.5\%$.

So, the correct answer is “Option B”.

Note: Students should carefully obtain values from the graph. Students should always remember basic formulas for calculating percentage and total marks. Students should not calculate the percentage of marks obtained by students in periodical exams of August, $01$ and October, $01$ separately and then take their average. We have to find a percentage of them together.