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The present ages of three persons in proportions $4 : 7 : 9$. Eight years ago, the sum of their ages was $56$. Find their present ages (in years).

  1. $8, 20, 28$
  2. $16, 28, 36$
  3. $20, 35, 45$
  4. None of the above options
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$\textrm{Assume there age ratio is x}$

$\textrm{then age of 3 person is $4x$,$7x$ ,$9x$}$

$\textrm{According to the question,8 year ago sum of their age was 56}$

$\Rightarrow$ $\textrm{$(4x-8)$+(7x-8)+(9x-8)=56}$

$\Rightarrow$ $20x-24=56$

$\Rightarrow$ $20x=80$

$\Rightarrow$ $x$ = $4$

$\textrm{Now their present age is16,28,36. Option B.}$
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