The ages of Aditi and her mother were both two-digit numbers comprising the same pair of digits. If fifteen years ago, Aditi’s age was one-third the age of her mother, find the sum of their present ages (in years)
Question
The ages of Aditi and her mother were both two-digit numbers comprising the same pair of digits. If fifteen years ago, Aditi’s age was one-third the age of her mother, find the sum of their present ages (in years)
Solution
To solve this problem, we need to make a few assumptions based on the information given:
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Aditi and her mother's ages are two-digit numbers with the same pair of digits. This means that if Aditi is xy years old, her mother is yx years old, where x and y are digits from 0 to 9.
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Fifteen years ago, Aditi's age was one-third of her mother's age. This means that (xy - 15) = 1/3 * (yx - 15).
Now, we need to find the values of x and y that satisfy this equation.
After trying different combinations, we find that x = 2 and y = 4 satisfy the equation. This means that Aditi is 24 years old and her mother is 42 years old.
So, the sum of their present ages is 24 + 42 = 66 years.
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