Question

In an examination, the number of those who passed and the number of those who failed were in the ratio $25:4.$ If five more had appeared and the number of failures were $2$ less than earlier, the ratio of those passed to failures would be $22:3.$ The number who appeared at the examination is

• A. $145$
• B. $150$
• C. $155$
• D. $180$

Answer 1

Answer: (A)

$145$

Let the number of those who passed = 25 x and number of failures = 4x
$\therefore$ Total no. of candidates who appeared = 29x
New number of candidates who appeared = 29x +5
New number of failures = 4x - 2
$\therefore$ New number of passed candidates = (29x + 5) - (4x - 2) = 25x + 7
Given, $\frac{25x+7}{4x-2}=\frac{22}{3}\Rightarrow 3(25x+7)=22(4x-2)$
$\Rightarrow 75x+21=88x-44\Rightarrow 13x=65\Rightarrow x=5$
$\therefore$ Total no. of the students who appeared at the examination $=29\times 5=145$