In an examination, the ratio of the number of candidates who passed to those who failed was 5 ∶ 2. If the number of failed candidates had been 14 more, then the ratio of the number of passed candidates to those who failed would have been 4 ∶ 3. The number of candidates who appeared in the examination was:?

Option 4 : 98

Given:

The passed to fail ratio = 5 : 2

When the number of failures is 14 more, then the passed to fail ratio would have been 4 : 3 

Calculation:

Let the successful candidates be 5x and the failure candidates be 2x.

According to Question,

(5x - 14)/(2x + 14) = 4/3 

⇒ 15x - 42 = 8x + 56

⇒ x = 98/7 = 14 

Total number of candidates who appeared for the examination = 5x + 2x = 7x = 7 × 14 = 98

∴ The number of candidates who appeared in the examination was 98

Alternate MethodTotal students = 5 + 2 = 7 units

When 14 more failed, total students = 4 + 3 = 7 units

5 ∶ 2

↓ 1 unit = 14 students

4 ∶ 3 

Total number of students = 7 units = 7 × 14 = 98 students

∴ The total number of students is 98.