Multiple choice

The ages of Hari and Harry are in the ratio $5:7$. If four years from now, the ratio of their ages will be $3:4$, then the present age of

  1. Hari is $20$ years and Harry is $28$ years.
  2. Hari is $28$ years and Harry is $20$ years.
  3. Hari is $25$ years and Harry is $35$ years.
  4. Hari is $35$ years and Harry is $25$ years.
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A Correct answer
Explanation

Let Hari's age be 5x and Harry's be 7x. Four years later, (5x+4)/(7x+4) = 3/4. Solving this gives 20x + 16 = 21x + 12, so x = 4. Thus, Hari is 20 and Harry is 28.

AI explanation

Let the present ages of Hari and Harry be 5x and 7x years based on the given 5 to 7 ratio. Four years from now, their ages will be 5x + 4 and 7x + 4, and the new ratio gives the equation 5x + 4 divided by 7x + 4 equals 3 divided by 4. Cross-multiplying yields 4 times 5x + 4 equals 3 times 7x + 4, which simplifies to 20x + 16 = 21x + 12. Solving this gives x = 4, so Hari is 5 times 4, which is 20 years, and Harry is 7 times 4, which is 28 years.

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