Question

The ratio of passed and failed students in an examination was 3 : 1. Had 30 less appeared and 10 less failed, the ratio of passes to failures would have been 13 : 4. Find the number of students who appeared for the examination.

Answer 1

Let the number of passed students be x and the number of failed students be y.
According to the question,
`x/y = (3)/(1)`
⇒ x = 3y         ....(i)
Now, if 30 less appeared and 10 less failed, then we have
Number of students appeared = x + y - 30
number of failed students = y - 10
∴ number of passed students = x - 20
⇒ `(x - 20)/(y - 10) = (13)/(4)`
⇒  4x - 80 = 13y - 130
⇒  4x - 13y = -50
⇒  4(3y) - 13y = -50         ...[From (i)]
⇒  12y - 13y = -50
⇒  -y = -50
⇒  y = 50
⇒  x = 3 x 50 = 150
⇒  x + y 
= 150 + 50
= 200
Hence, 200 students appeared for the examination.