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elect the correct answerA man's age is 125% of what it was 10 years ago, but 83 1/3% of what it will be after 10 years. What is his present age?Options60504070

Question

elect the correct answerA man's age is 125% of what it was 10 years ago, but 83 1/3% of what it will be after 10 years. What is his present age?Options60504070

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Solution

Let's solve this step by step:

  1. Let's assume the man's present age is X years.

  2. According to the problem, his age 10 years ago was 100% of his age at that time. Now, his age is 125% of what it was 10 years ago. So, we can write this as: X = 125% of (X-10).

  3. In mathematical terms, this becomes: X = 1.25 * (X - 10).

  4. Simplifying this equation, we get: X = 1.25X - 12.5.

  5. If we move the terms around, we get: 0.25X = 12.5.

  6. Solving for X, we find: X = 12.5 / 0.25 = 50.

  7. Now, let's check the second condition. His present age is 83 1/3% of what it will be in 10 years. So, we can write this as: X = 83.33% of (X + 10).

  8. In mathematical terms, this becomes: X = 0.8333 * (X + 10).

  9. Simplifying this equation, we get: X = 0.8333X + 8.333.

  10. If we move the terms around, we get: 0.1667X = 8.333.

  11. Solving for X, we find: X = 8.333 / 0.1667 = 50.

So, the man's present age is 50 years. Therefore, the correct answer is 50.

This problem has been solved

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