Question

In an examination, the ratio of passes to failures was 4 : 1. If 30 less had appeared and 20 less passed, the ratio of passes to failures would have been 5 : 1. How many students appeared for the examination

Answer 1

Let the number of passes = 4x
and number of failures = x
The total number of students appeared = 4x + x = 5x
In the second case, the number of students appeared = 5x – 30
and number of passes = 4x – 20
∴ No. of failure
= (5x – 30) - (4x – 20)
= 5x - 30 – 4x + 20
= x – 10
According to the condition
`(4x - 20)/(x - 10) = (5)/(1)`
⇒ 5x - 50 = 4x - 20
⇒ 5x - 4x = -20 + 50
⇒ x = 30
∴ Number of students appeared = 5x
= 5 x 30
= 150.