Question

In an examination, the ratio of passes to failures was 4 : 1. Had 30 less appeared and 20 less passed, the ratio of passes to failures would have been 5 : 1. Find the number of students who appeared for the examination.

Answer 1

Let the no. of pass candidates be x
and the no. of fail candidates be y.

According to the question,
`x/y = 4/1`
x - 4y = 0                                     ...(1)
and
`[ x - 20 ]/[ y - 10 ] = 5/1`
x - 5y = -30                                 ...(2)

Subtracting equation (2) from (1),
    x - 4y = 0
-   x - 5y = - 30  
    -    +       +     
          y = 30

From (1)
x - 4(30) = 0
x = 120

Total students appeared = x +  y = 120 + 30 = 150.