The average age of a husband and wife at the time of their marriage was $25$ years. A son was born to them two years after their marriage. The present average age of all three of them is $24$ years. How many years is it since the couple got married?

### Concept & Formula This problem requires forming an algebraic equation where the elapsed time is the unknown variable. Express the present ages of all family members in terms of the number of years since marriage. $$ \text{Present Age} = \text{Age at Marriage} + \text{Years Since Marriage} $$ ### Step-by-Step Solution * **Given:** * Average age of Husband ($H$) and Wife ($W$) at marriage = $25$ * Son was born $2$ years after marriage. * Present average age of $H, W,$ and Son = $24$ * **Calculation:** Let the number of years since the couple got married be $x$. Total age of Husband and Wife at marriage: $$ 25 \times 2 = 50 \text{ years} $$ Present total age of Husband and Wife (since $x$ years have passed for both): $$ 50 + 2x $$ Since the son was born $2$ years after marriage, his present age is: $$ x - 2 $$ The present average age of all $3$ members is $24$, meaning their present total age is: $$ 24 \times 3 = 72 \text{ years} $$ Set up the final equation by summing the family's current ages: $$ (50 + 2x) + (x - 2) = 72 $$ $$ 3x + 48 = 72 $$ $$ 3x = 24 $$ $$ x = 8 $$ ### Exam Strategy & Shortcut Use Option Elimination to save time. Test option (c) $8$ years. If they married $8$ years ago, their current total age is $50 + (2 \times 8) = 66$. If they married $8$ years ago, the son ($2$ years younger than the marriage) is $6$ years old. Total family age = $66 + 6 = 72$. Average = $72 / 3 = 24$. This matches the question perfectly. ### Common Pitfall A major trap is defining the son's age as simply $x$ or assuming he is the same age as the marriage. Because he was born $2$ years *after* the marriage, his age is $(x - 2)$. Forgetting this subtraction will ruin the algebraic setup. ### Final Answer **Therefore, the correct answer is 8 years.**