Question : If 50 fewer had applied and 25 fewer selected, the ratio of selected to rejected would have been 9 : 4. So, how many candidates had applied if the ratio of selected to rejected was 2 : 1?
Option 1: 125
Option 2: 250
Option 3: 375
Option 4: 500
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Correct Answer: 375
Solution :
The ratio of selected to rejected was 2 : 1.
Let selected candidates = $2x$, rejected candidates = $x$ and total candidates = $3x$.
If 50 less had been applied and 25 less selected, the ratio of selected to rejected would be 9 : 4.
So, the total candidates = $(3x - 50)$
and selected candidates = $(2x - 25)$ and rejected candidates = $(3x - 50)-(2x - 25)=x - 50 + 25=(x-25)$
According to the question,
$\frac{(2x - 25)}{(x - 25)}=\frac{9}{4}$
$\therefore x = 125$
Total number of candidates who applied $=3x = 3×125= 375$
Hence, the correct answer is 375.
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