Discussion
15 years ago, the mother's age was twice the daughter's age. If 3 years from now, the sum of their ages will be 99, what is the difference between their present ages ?
Answer: B
The difference between their present ages is 21 years.
Let the mother's present age be \(m\) and the daughter's \(d\).
\[ \begin{aligned} m - 15 &= 2(d - 15) \\ m &= 2d - 15 \end{aligned} \]
Three years from now their ages add up to 99:
\[ \begin{aligned} (m+3) + (d+3) &= 99 \\ m + d &= 93 \\ (2d - 15) + d &= 93 \\ d &= 36,\ m = 57 \end{aligned} \]
So the difference is \(57 - 36 = 21\) years. As a check, 15 years ago they were 42 and 21, and 42 is twice 21. The difference between two ages never changes, so the other options cannot be right once 42 and 21 check out.
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