The average of marks obtained by 100 candidates in a certain examination is 40. If the average marks of passed candidates is 55 and that of failed candidates is 35, what is the ratio of number of students passed in the examination to that who failed?

Let the number of students who passed the examination be ‘x’. Number of students who failed in the examination = 100 – x Total marks obtained by 100 candidates = 100 × 40 Total marks of passed candidates = 55x Total marks of failed candidates =35 × (100 - x) Total marks obtained by 100 candidates = Total marks of passed candidates + Total marks of failed candidates 100 × 40 = 55x + 35 × (100 - x) 55x + 35 × 100 – 35x = 100 × 40 20x = 100 × 40 – 100 × 35 20x = 100 × 5, x = 25 So, number of passed candidates = 25 Number of failed candidates = 100 – x = 100 – 25 = 75 Required ratio = 25: 75 = 1:3