Multiple choice

Ten years ago, the age of a man was 20 years less than 6 times his son's age. Ten years hence, his age will be 30 years less than thrice his son's age. After how many years from now will their combined age be 90 years?

  1. 5

  2. 10

  3. 15

  4. 20
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the man's current age be m and son's current age be s. From 10 years ago: m-10 = 6(s-10) - 20, giving m = 6s - 70. From 10 years hence: m+10 = 3(s+10) - 30, giving m = 3s - 10. Solving: 6s - 70 = 3s - 10, so 3s = 60 and s = 20. Then m = 50. Current combined age is 70. After x years: 70 + 2x = 90, so x = 10.

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