Multiple choice

The ratio of the ages of A and B ten years before was $3 : 5$. The ratio of their present ages is $2 : 3$ . Their ages are respectively

  1. $30,50$
  2. $20,30$
  3. $40,60$
  4. $16,24$
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C Correct answer
Explanation

Let ages be 2x and 3x. 10 years ago: (2x-10)/(3x-10) = 3/5. 10x - 50 = 9x - 30. x = 20. Ages are 2(20)=40 and 3(20)=60.

AI explanation

Let the present ages of A and B be 2x and 3x years according to their given ratio. Ten years before, their ages were 2x minus 10 and 3x minus 10, and the ratio of these ages is 3 is to 5. Solving the equation 2x minus 10 divided by 3x minus 10 equals 3 divided by 5 gives 5 times 2x minus 10 equals 3 times 3x minus 10, which simplifies to 10x minus 50 equals 9x minus 30. Solving for x gives x equals 20, so the present ages of A and B are 2 times 20 and 3 times 20, which are 40 and 60 years respectively.

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