Multiple choice

The age of a man 10 years ago was thrice the age of his son. 10 years hence, the man's age will be twice the age of his son. The ratio of their present ages is ?

  1. 7:3

  2. 5:2

  3. 9:2

  4. 13:4

  5. None of these
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A Correct answer
Explanation

Let man's age be M and son's be S. 10 years ago: M-10 = 3(S-10) => M-3S = -20. 10 years hence: M+10 = 2(S+10) => M-2S = 10. Subtracting equations: S = 30. Then M = 70. Ratio M/S = 70/30 = 7:3.

AI explanation

Let the present age of the son be x years and the father be y years. The first equation is y minus 10 equals 3 times (x minus 10), which simplifies to y equals 3x minus 20. The second equation is y plus 10 equals 2 times (x plus 10), which simplifies to y equals 2x plus 10, and setting them equal gives x equals 30 and y equals 70, resulting in a ratio of 7:3.

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