Five years ago, A was 10 years younger than B. What will be the difference between their ages after 2 years from now?A3 YearsB8 YearsC10 YearsD15 Years

1. Break Down the Problem

Let’s define the current ages of A and B:

• Let $A$ be the current age of person A.
• Let $B$ be the current age of person B.

Five years ago, A was 10 years younger than B. This information can be written as: $A - 5 = (B - 5) - 10$

We need to find the difference between their ages after 2 years. Therefore: $\text{Difference in ages after 2 years} = (A + 2) - (B + 2) = A - B$

2. Relevant Concepts

From the equation $A - 5 = B - 15$:

1. Rearranging gives us: $A - B = -10$

Now we know the current difference in ages is: $A - B = -10 \implies B - A = 10$

3. Analysis and Detail

The difference in ages will not change over time. Therefore, the difference between their ages after 2 years will still be $10$ years.

4. Verify and Summarize

Hence, $B$ will always be $10$ years older than $A$. After analyzing and confirming our calculations, we conclude that:

Final Answer

The difference between their ages after 2 years will be 10 Years.