GATE Mechanical 2020 Set 1 | GA | Question: 10

Question

The bar graph shows the data of the students who appeared and passed in an examination for four schools $P, Q, R$, and $S$. The average of success rates $\text{(in percentage)}$ of  these four schools is _______.

• A. $58.5\%$
• B. $58.8\%$
• C. $59.0\%$
• D. $59.3\%$

Comments

Success Rate (or Pass Percentage) for a school
\[
\text{Success Rate} = \left( \frac{\text{Number of Passed Students}}{\text{Number of Appeared Students}} \right) \times 100
\]
If there are \(n\) schools, :
\[
\text{Average} = \frac{\text{Sum of individual success rates}}{n}
\]
 

Answer 1

We can calculate the success rate of every school, then find their average. 

Success rate $ = \dfrac{\text{Number of students who passed the exams}}{\text{Number of appeared students}}$

• Success rate of school $P = \dfrac{280}{500} \times 100\%  = 56\%.$
• Success rate of school $Q = \dfrac{330}{600} \times 100\%  = 55\%.$
• Success rate of school $R = \dfrac{455}{700} \times 100\%  = 65 \%.$
• Success rate of school $S = \dfrac{240}{400} \times 100\%  =  60\%.$

Now, the average success rates of all the schools $ = \dfrac{56\% + 55\% + 65\%  + 60\%}{4} =  \dfrac{236\%}{4} = 59.0\%.$ 

So, the correct answer is $(C).$