Multiple choice

The present age of A is twice that of B. After 30 years from now the age of A will be $\displaystyle 1^{1/2}$ times that of B. Find the present ages of A and B respectively.

  1. $60, 30$
  2. $30, 60$
  3. $40, 50$
  4. $50, 40$
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A Correct answer
Explanation

Let the present ages of A and B be 2x and x. After 30 years, their ages will be 2x+30 and x+30. The problem states 2x+30 = 1.5(x+30), which simplifies to 2x+30 = 1.5x+45, so 0.5x = 15, meaning x = 30. Thus, A is 60 and B is 30.

AI explanation

Let the present age of B be x years, making A's present age 2x years. The problem states that after 30 years, the age of A will be 1.5 times the age of B, which gives the linear equation 2x + 30 = 1.5(x + 30). Simplifying this yields 2x + 30 = 1.5x + 45, meaning 0.5x = 15, so x = 30. Therefore, the present ages of A and B are 60 and 30 respectively.

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