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Question : In an army selection process, the ratio of selected to unselected candidates was $4:1$. If 90 fewer candidates had applied and 20 fewer were selected, the ratio of selected to unselected candidates would have been $5:1$. How many candidates had applied for the process?

Option 1: 1650

Option 2: 3300

Option 3: 825

Option 4: 4950


Team Careers360 4th Jan, 2024
Answer (1)
Team Careers360 19th Jan, 2024

Correct Answer: 1650


Solution : Let the selected and unselected candidates be $4x$ and $x$
Total number of candidates = $5x$
If 90 fewer candidates had applied, the total number of candidates = $5x - 90$
If 20 fewer were selected, the number of selected candidates then = $4x - 20$
So, number of unselected candidates = Total number of candidates - Number of selected candidates.
= $5x - 90 - (4x-20)$
= $x-70$
New ratio: $\frac{(4x-20)}{(x-70)}=\frac{5}{1}$
⇒ $x=330$
Total number of candidates applied = $5x$ = 1650.
Hence, the correct answer is 1650.

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