Ladies' Diary/Ratios of Ages of Groom to Bride

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Puzzle

A person remarked that upon his wedding day the proportion of his own age to that of his bride was $3$ to $1$,
but $15$ years afterwards the proportion of their ages was $2$ to $1$.
What were their ages upon the day of their marriage?


Solution

The bride was $15$ and the groom was $45$ when they married.

Outrageous.


Proof

Let $x$ and $y$ be the ages of the bride and groom at their marriage respectively.

We have:

\(\ds 3 x\) \(=\) \(\ds y\)
\(\ds 2 \paren {x + 15}\) \(=\) \(\ds y + 15\)
\(\ds \leadsto \ \ \) \(\ds 2 x + 30\) \(=\) \(\ds 3 x + 15\)
\(\ds \leadsto \ \ \) \(\ds x\) \(=\) \(\ds 15\)
\(\ds \leadsto \ \ \) \(\ds y\) \(=\) \(\ds 45\)

$\blacksquare$


Sources