Multiple choice

$Let the present ages of the three persons be (4x), (7x), and (9x). Eight years ago, their ages were (4x - 8), (7x - 8), and (9x - 8). The sum of their ages eight years ago was 56. Therefore, we have the equation: ( (4x - 8) + (7x - 8) + (9x - 8) = 56 )$ $Simplifying the equation, we get: ( 20x - 24 = 56 )$ $Adding 24 to both sides, we have: ( 20x = 80 )$ $Dividing both sides by 20, we get: ( x = 4 )$ $Therefore, their present ages are: ( 4x = 4(4) = 16 ), ( 7x = 7(4) = 28 ), and ( 9x = 9(4) = 36 )$

  1. $20, 35, 45$
  2. $16, 28, 36$
  3. $8, 20, 28$
  4. $8, 14, 18$
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B Correct answer
Explanation

The ages are in ratio 4:7:9, so let present ages be 4x, 7x, 9x. Eight years ago, their ages were 4x-8, 7x-8, 9x-8 with sum 56. Solving 20x-24=56 gives x=4. Present ages are 16, 28, 36. Option A (20,35,45) is 4x,7x,9x with x=5 but doesn't satisfy the 8-years-ago condition. Options C and D are incorrect calculations.

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