A mother's age is double her son's age at present. If the difference of their ages after 24 years from now is 20, then find their ages at present (in years), respectively.
40, 20
Let's solve the given problem step-by-step:
- x be the present age of the son.
- Then, the mother's current age will be 2x since she is twice as old as her son at present.
- The question states that after 24 years, the difference in their ages will be 20 years. This can be written as: (2x + 24) - (x + 24) = 20.
-
Simplify the equation:
2x + 24 - x - 24 = 20x = 20.
- Therefore, the present age of the son is 20 years.
- Substitute x = 20 in the mother's age equation: 2x = 2 \times 20 = 40.
- Hence, the mother's current age is 40 years.
Therefore, the present ages of the mother and son, respectively, are 40 and 20 years. This corresponds to the option 40, 20.
Justification for Other Options:
- For option 46, 23: If the son's age is 23, then the mother's age should be 2 \times 23 = 46. However, after 24 years, the difference becomes 46 + 24 - (23 + 24) = 23, hence it does not satisfy the condition.
- For option 54, 28: Similarly, after 24 years, the age difference would be more than 20 years, invalidating this option.
- For option 38, 19: After 24 years, the age difference would become 38 + 24 - (19 + 24) = 19, which does not meet the condition of 20.
Thus, the correct answer is indeed 40, 20.
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