Question : In an examination, the number of students who passed and the number of students who failed were in the ratio 25 : 4. If one more student had appeared and passed and the number of failed students was 3 less than earlier, the ratio of passed students to failed students would have become 22 : 3. What is the difference between the number of students who, initially, passed the examination and the number of students who failed the examination?
Option 1: 132
Option 2: 126
Option 3: 174
Option 4: 150
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Correct Answer: 126
Solution : Let the initial number of students who passed be $25x$ and the number of students who failed be $4x$, where $x$ is a constant. If one more student had appeared and passed and the number of failed students was 3 less than earlier, the ratio of passed students to failed students would have become 22 : 3. $⇒\frac{29x + 1}{4x - 3} = \frac{25}{3}$ $⇒87x + 3 = 100x - 75$ $⇒x = 6$ Therefore, the difference between the number of students who initially passed the examination and the number of students who failed the examination is $25x - 4x= 21x=21\times6=126$. Hence, the correct answer is 126.
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