The number of those who passed and failed in an examination was in the ratio of 25 ∶ 4. Now if one more student appears for the exam and the number of failed students are reduced by 3 than before, then the ratio becomes 22 ∶ 3. Find the number of students who appeared in the examination initially:?

Option 1 : 174

Given:

Passed and failed students ratio is 25 ∶ 4

If 1 more student appears and failed student reduces to 3, then the ratio becomes 22 ∶ 3.

Calculations:

Let passed and failed candidates be x and y respectively

⇒ x/y = 25/4

⇒ 4x = 25y      ----(1)

According to the question, we have

In the second case, Number of students appeared = x + y + 1

and, Number of those who failed = y - 3

So, Number of passed candidates = x + y + 1 - (y - 3)

⇒ Number of passed candidates = x + 4

Ratio of passed to failed candidates is 22 ∶ 3

⇒ (x + 4)/(y - 3) = 22/3

⇒ 3x + 12 = 22y - 66

⇒ 22y - 3x = 78

Put x = 25y/4 from (1) in equation, we get

⇒ 22y - 3(25y/4) = 78

⇒ 88y - 75y = 312

⇒ y = 24

Put y = 24 in equation (1), we get

⇒ x = (25/4) × 24

⇒ x = 150 students

Total number of students appeared initially is 

Total students = x + y

⇒ 150 + 24

⇒ 174 students

∴ Total number of students initially is 174 students.

Shortcut Trick Initial pass to fail ratio = 25 : 4

Total students = 25 + 4 = 29      -----(i)

Final pass to fail ratio = 22 : 3

Total students = 25      -----(ii)

But according to question 1 new student admitted

Multiply (i) by 6 and (ii) by 7

So initial number of students = 29 × 6 = 174

∴ Total number of students initially is 174 students.