One year ago, the father was 8 times as old as his son. Now his age is the square of his son’s age. Find their present ages.

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One year ago, the father was 8 times as old as his son. Now his age is the square of his son’s age. Find their present ages.

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Present age of a father is 36 years and that of his son is 6 years.

Present age of the father is 49 years and that of his son is 7 years.

Present age of the father is 64 years and that of his son is 8 years.

Present age of the father is 25 years and that of his son is 5 years.

answer is B.

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Detailed Solution

Concept: Assume that the father is x years old and the son is y. Find the relationships or equations between x and y that satisfy the above constraints, then solve them to obtain the solutions.
The age difference between the father and son is indicated in the question. One year ago, the father was eight times older than his son, and today, the father's age is equal to the square of his son's age. Now that the requirements have been established, we can find the father and son's ages and so answer the question. Let's assume that the father is x years old and the son is y years old. Now, taking condition 1, we obtain the father's age to be x-1 and the son's age to be y-1, allowing us to write it as,

Applying the second condition now, we can state that the father is x years old and the son is y, allowing us to write it as,

We can deduce that x=8y-7 from the first condition. therefore when we replace it, we get,

Taking (8y-7) now from the right to the left, we obtain,
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Consequently, y can have a value between 1 and 7. One year is not a valid value because it does not meet any of the requirements. Therefore, y, or the son's age, will be seven years. then x, or the father's age, will be

Hence, the correct answer is 2.

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