In an army selection process, the ratio of selected to unselected candidates was 6:1. If 30 less had applied and 10 less selected, the ratio of selected to unselected would have been 7:1. How many candidates had applied for the process?

• 910
  
  Let number of candidates selected=x, unselected=y, then total candidates=x+y and
  Ratio of selected to unselected=x/y=6/1 => x=6y ---(i)
  When 30 less applied, total candidates=x+y-30 and candidates selected=x-10
  So unselected candidates=(x+y-30) - (x-10) = y-20
  Now ratio of selected to unselected=(x-10) / (y-20) = 7/1
  => x - 7y = -130 ---(ii)
  Solving (i) & (ii), x=780, y=130
  Hence candidates applied = total candidates=x+y=780+130=910
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