Multiple choice

The ages of Han and Harry are in the ratio $5 : 7$. Four years from now, the ratio of their ages will be $3 : 4$. Find their present ages.

  1. Present age of Han $= 15 $years

    Present age of Harry $=21 $years
  2. Present age of Han $ =25 $years

    Present age of Harry $=35$years
  3. Present age of Han $= 20$ years

    Present age of Harry $=28$years
  4. Present age of Han $= 25 $years

    Present age of Harry $=30 $years
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C Correct answer
Explanation

Let ages be 5x and 7x. (5x+4)/(7x+4) = 3/4. 20x + 16 = 21x + 12, so x = 4. Ages are 20 and 28.

AI explanation

Let the common ratio factor be x, so Han's present age is 5x and Harry's present age is 7x. Four years from now, the ratio of their ages will be 3 to 4, yielding the proportion (5x + 4) / (7x + 4) = 3 / 4. Cross-multiplying gives 4(5x + 4) = 3(7x + 4), which simplifies to 20x + 16 = 21x + 12, meaning x = 4. Han's present age is 5 times 4, or 20 years, and Harry's present age is 7 times 4, or 28 years.

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