The number of those who passed and failed in an examination was in the ratio 23 ∶ 4. If eleven more students appeared for the examination and the number of those who failed was 4 less than before, the ratio of passed and failed became 22 ∶ 3. Find the number of students who appeared in the exam initially:?

Option 3 : 189

Given:

The ratio of number of passed and failed students = 23 ∶ 4

Number of students more appeared in examination = 11

Number of students who failed = 4 less than before

New ratio of passed to failed students = 22 ∶ 3

Calculation:

Let the number of passed and failed students be 23x and 4x respectively

Total students = 23x + 4x = 27x

After admitting 11 more students, Total students = 27x + 11

New failure students = 4x - 4

New ratio of passed to failed students = 22 ∶ 3 = 22y : 3y

Total students = 25y

According to the question

The ratio of failed to total students appeared = (4x - 4) ∶ (27x + 11) = 3y ∶ 25y

⇒ (4x - 4) × 25y = (3y) × (27x + 11)

⇒ 100x - 100 = 81x + 33

⇒ 19x = 133

⇒ x = 7

Number of students initially = 27x = 27 × 7

⇒ 189

∴ The number of students who appeared in exam initially was 189.