The difference between the ages of two men is 10 years. 15 years ago, the elder one was twice as old as the younger one. The present age of the elder man is

### Concept & Logic The golden rule of age problems applies perfectly here: **The difference in age between two individuals remains constant throughout their lives.** If the difference is 10 years today, it was also exactly 10 years 15 years ago. ### Step-by-Step Solution * **Given:** 15 years ago, the elder man was twice as old as the younger man. * Let the younger man's age 15 years ago be $x$. * Then, the elder man's age 15 years ago was $2x$. * **Calculation:** We know the age difference is always 10 years. We can express this using their ages from 15 years ago: $$ \text{Elder} - \text{Younger} = 10 $$ $$ 2x - x = 10 \implies x = 10 $$ * So, 15 years ago, the younger man was 10 years old, and the elder man was $2(10) = 20$ years old. * **Finding Present Age:** The question asks for the present age of the elder man. * Present Age = (Age 15 years ago) + 15 * Elder man's present age = $20 + 15 = 35$ years. ### Exam Strategy & Shortcut This problem should take 5 seconds. Whenever one person is "twice as old" as another, the *difference* in their ages is exactly equal to the *younger person's age* ($2x - x = x$). Since the difference is 10, the younger person was 10 at that time. The elder was $10 \times 2 = 20$. Add 15 years to get the present age: $20 + 15 = 35$. No written algebra required! ### Common Pitfall A standard trap is solving for the age 15 years ago (20 years) and hastily marking it as the final answer if it were an option. Always re-read the final sentence of the question to confirm whether it asks for the *past*, *present*, or *future* age. ### Final Answer **Therefore, the correct answer is 35 years.**