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The ratio between the ages of Ajay and Vijay at present is $2: 3.$ Ajay is $6$ years younger than Vijay. The ratio of Ajay's age to Vijay's age after $6$ years will be :

  1. $2: 3$
  2. $1: 2$
  3. $4: 3$
  4. $3: 4$
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