Question : In an entrance examination at different centres, a total of 25, 30, 40, 45, 60 and 100 students appeared. The pass percentages of the different centres are 20%, 30%, 35%, 40%, 50% and 75%, respectively. The pass percentage of the entrance examination is: (correct to the nearest integer)
Option 1: 59%
Option 2: 43%
Option 3: 53%
Option 4: 50%
Correct Answer: 50%
Solution :
Passing percentage = $\frac{\text{Number of students passed in the examination at all centres}}{\text{Total number of students appeared}}\times 100$
⇒ Passing percentage = $\frac{\text{20% of 25 + 30% of 30 + 35% of 40 + 40% of 45 + 50% of 60 + 75% of 100}}{25 + 30 + 40 + 45 + 60 + 100} × 100$
= $\frac{5 + 9 + 14 + 18 + 30 + 75}{300} × 100$
= $\frac{151}{300} × 100$
= $50.33\% \approx 50\%$
Hence, the correct answer is 50%.
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