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.

• A. 150
• B. 140
• C. 130
• D. 120

Answer 1

The correct option is A 150

Suppose $x$ candidates passed and $y$ failed; therefore,
$\frac{x}{y}=\frac{4}{1}$
$x=4y$ (1)
In the second case; no. of students appeared $=x+y-30$

and no. of those who passed $=x-20$

No of failed
$N=x+y-30-(x-20)$
$N=y-10$
from the question
$\frac{x-20}{y-10}=\frac{5}{1}$
$x-20=5y-50$
$x-5y=-30$
from ( 1)
$4y-5y=-30$
$y=30$
$x=120$
So, $x+y=150$
Total number of students who appeared for the examination $=150$