Question : In a certain school, 10% of the students have less than 75% attendance and are not allowed to sit in the exam, but 20% of the students who have less than 75% attendance are allowed to sit in the exam. What percentage of students in the school have less than 75% attendance?
Option 1: 30%
Option 2: 12.5%
Option 3: 15%
Option 4: 10.5%
Correct Answer: 12.5%
Solution :
Let the total number of students be $m$.
Let the number of students having less than 75% attendance be $n$.
Percentage of students having less than 75% attendance and are not allowed to sit in the exam = 10%
Percentage of students who have less than 75% attendance and are allowed to sit in the exam = 20%
So, 100% – 20% = 80% of the students who have less than 75% attendance are not allowed to sit in the exam.
According to the question,
10% of $m$ = 80% of $n$
⇒ $\frac{10m}{100}=\frac{80n}{100}$
⇒ $\frac{n}{m}=\frac{1}{8}=12.5$%
The number of students in the school who have less than 75% attendance is 12.5%.
Hence, the correct answer is 12.5%.
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