Multiple choice

Aman and Ankit's present ages are 'x' years and 'y' years, respectively. If Aman's age will be 5 year more than half of Ankit's age 3 years from now, then find the linear equation that represents the correct relation regarding the present age of Aman and Ankit.

  1. 2x - 7 = y

  2. 2x + y = 7

  3. 2x - 6 = y

  4. 2x - 5 = y

  5. 2x - y = 6
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A Correct answer
Explanation

Aman = x, Ankit = y. 3 years from now, Ankit's age = y+3. Aman's age 3 years from now = x+3. Relation: x+3 = 0.5(y+3) + 5. Multiply by 2: 2x+6 = y+3+10 -> 2x+6 = y+13 -> 2x-7 = y.

AI explanation

In three years, their ages will be (x + 3) and (y + 3). The given condition yields the equation (x + 3) = (y + 3)/2 + 5. Multiplying the entire equation by 2 to clear the fraction gives 2x + 6 = y + 3 + 10, which simplifies to 2x - 7 = y.

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