In an army selection process, the ratio of selected to unselected was 3:1. If 60 less had applied and 30 less selected, the ratio of selected to unselected would have been 5:1. How many candidates had applied for the process?

Let the number of selected candidates be 3k and unselected candidates be 1k.
Total applied candidates initially = 3k+1k=4k.

According to the second condition:
New number of total applied candidates = 4k−60
New number of selected candidates = 3k−30

Therefore, the new number of unselected candidates = Total applied−Selected

New unselected=(4k−60)−(3k−30)=4k−60−3k+30=k−30
The new ratio of selected to unselected is given as 5:1:

k−30
3k−30
​
=
1
5
​

3k−30=5(k−30)
3k−30=5k−150
5k−3k=150−30
2k=120
k=60
Total number of candidates who initially applied = 4k=4×60=240.