Question

How many students of institutes M and S are studying at graduate level?

A. 7516
B. 8463
C. 9127
D. 9409

Answer 1

Hint: We here need to find the total number of graduation level students studying in institutes M and S. For this, we will first see the pie chart which is having information about the graduation level students. Then, we will see what percentage of students are studying in institutes M and S. Then we will calculate the number of students of both the institutes separately studying at graduate level using their percentage out of the total and the total number of students in graduation, i.e. 27300. Then we will add them and hence obtain our answer.

Complete step-by-step answer:
We here need to calculate the total number of students studying in institutes M and S. For this, we will have to look at the pie chart of students of graduate level.
The required pie chart then is:

Now, we have been given that the total number of students of graduation level are 27300.
Now, if we read the required pie chart, we can see that the percentage of students of graduation level studying in institute M is 17% and that of S is 14%.
Thus, the total students of graduation level studying in institute M and S is the sum of 12% of and 14% of the total students studying in the graduation level, i.e. 27300
Thus, the number of students studying in institute M are given as:
17% of total graduation level students
$\begin{align}
  & \Rightarrow 17\%\text{ of 27300} \\
 & \Rightarrow \dfrac{17}{100}\times 27300 \\
 & \Rightarrow 4641 \\
\end{align}$
Thus, the total number of students studying in institute M are 4641.
Similarly, the number of students studying in institute S are given as:
14% of total graduation level students
$\begin{align}
  & \Rightarrow 14\%\text{ of }27300 \\
 & \Rightarrow \dfrac{14}{100}\times 273 \\
 & \Rightarrow 3822 \\
\end{align}$
Thus, the total number of students studying in institute S are 3822.
Hence, the total number of students studying in institutes M and S are:
$\begin{align}
  & \Rightarrow 4641+3822 \\
 & \therefore 8463 \\
\end{align}$
Thus, the total number of students studying in institutes M and S are 8463.

So, the correct answer is “Option B”.

Note: We here calculated the number of students of institute M and S separately and then added them but we can directly calculate them together by adding both the percentages as:
The total percentage of students studying in institutes M and S are given as:
$17\%+14\%=31\%$
Thus, the total number of students studying in institutes M and S are given as:
31% of total graduation level students
$\begin{align}
  & \Rightarrow 31\%\text{ of }27300 \\
 & \Rightarrow \dfrac{31}{100}\times 27300 \\
 & \Rightarrow 8463 \\
\end{align}$