Let's denote the present age of the daughter as \( d \) years. Then, the present age of the mother is \( 2.5d \) years.
According to the problem, four years ago, the daughter's age was \( d - 4 \) years, and the mother's age was \( 2.5d - 4 \) years. At that time, the ratio of their ages was 3:1, which gives us the equation:
\[ \frac{2.5d - 4}{d - 4} = 3 \]
To eliminate the fraction, we can cross-multiply:
\[ 2.5d - 4 = 3(d - 4) \]
Expanding the right side:
\[ 2.5d - 4 = 3d - 12 \]
Now, let's rearrange the equation to isolate \( d \):
\[ 2.5d - 3d = -12 + 4 \]
\[ -0.5d = -8 \]
Dividing both sides by -0.5:
\[ d = 16 \]
Now that we have the daughter's age, we can find the mother's age:
\[ \text{Mother's age} = 2.5d = 2.5 \times 16 = 40 \]
Thus, the present age of the mother is \( \boxed{40} \) years.
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