Question

The difference between ages of 2 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

• A. 35 years
• B. 25 years
• C. 38 years
• D. 45 years

Hint:

Instead of solving equations, you can quickly test the options. If the elder is 35, the younger is 25. 15 years ago, they were 20 and 10. Since 20 is $2 \times 10$, Option A is instantly verified.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Problems concerning ages are modeled using linear equations.
A crucial constant to keep in mind is that the difference in age between two individuals remains constant throughout their lives.
Key Formula or Approach:
Let the present age of the elder man be $E$ and the present age of the younger man be $Y$.
Set up a system of linear equations based on the conditions given:
1. $E - Y = 10$
2. $(E - 15) = 2 \cdot (Y - 15)$

Step 2: Detailed Explanation:
From the first condition, we know the difference in age is 10 years: \[ E - Y = 10 \implies Y = E - 10 \quad \text{--- (Equation 1)} \] From the second condition, 15 years ago, the elder one was twice as old as the younger one.
The age of the elder man 15 years ago was $E - 15$.
The age of the younger man 15 years ago was $Y - 15$.
We write this relationship as: \[ E - 15 = 2 \cdot (Y - 15) \quad \text{--- (Equation 2)} \] Substitute Equation 1 into Equation 2: \[ E - 15 = 2 \cdot ((E - 10) - 15) \] Simplify the terms inside the parentheses: \[ E - 15 = 2 \cdot (E - 25) \] Expand the right side: \[ E - 15 = 2E - 50 \] Rearrange terms to isolate the variable $E$: \[ 50 - 15 = 2E - E \] \[ E = 35 \] Thus, the present age of the elder man is 35 years.
Let us verify this result:
- Elder man's age is 35 years.
- Younger man's age is $35 - 10 = 25$ years.
- 15 years ago, the elder man was $35 - 15 = 20$ years old.
- 15 years ago, the younger man was $25 - 15 = 10$ years old.
Since 20 is indeed twice of 10, the conditions are satisfied.

Step 3: Final Answer:
The present age of the elder man is 35 years.