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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?

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? Correct Answer 126

Given:

Initially Passed : Failed = 25 : 4

Initially Appeared : Failed = 29 : 4

New passed and failed ratio = 22 : 3

New Appeared : Failed = 25 : 3

Concept used: 

Total number of student appeared = Pass student + Fail Student

Calculation:

Let Initially the number of students passed and failed the examination be 25x and 4x

Total number of student appeared = 25x + 4x = 29x

According to the question,

(29x + 1)/(4x - 3) = 25/3

⇒ 3(29x + 1) = 25(4x - 3)

⇒ 87x + 3 = 100x - 75

⇒ 13x = 78

⇒ x = 6

So,

Difference = 25x - 4x = 21x

Actual = 21 × 6 = 126

∴ The required difference is 126.

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