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ln an examination, the number of students who passed and the number of students who failed were in the ratio 25 : 4. If one more students 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?
Answer & Solution
Correct Answer:
Option
C
Ratio of passed student to fails students = Pass : Fail = 25x : 4x
Total number 25x + 4x = 29x
New ratio of passed student to fails students = Pass : Fail = 22x : 3x = 25x
$$\frac{{{\text{Fail}}}}{{{\text{Total}}}} = \frac{{4x - 3}}{{29x + 1}} = \frac{3}{{25}}$$
100x - 75 = 87x + 3
13x = 78
x = 6
So, the difference is = 25x - 4x
= 21x
= 21 × 6
= 126
Total number 25x + 4x = 29x
New ratio of passed student to fails students = Pass : Fail = 22x : 3x = 25x
$$\frac{{{\text{Fail}}}}{{{\text{Total}}}} = \frac{{4x - 3}}{{29x + 1}} = \frac{3}{{25}}$$
100x - 75 = 87x + 3
13x = 78
x = 6
So, the difference is = 25x - 4x
= 21x
= 21 × 6
= 126
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