Step 1: Understanding the Question:
This is an age-related word problem involving ratios and time offsets. We need to find the present age of Raju's sister based on her age difference with Raju at the time of his marriage, which happened 8 years ago.
Step 2: Key Formula or Approach:
Set up a linear equation for Raju's age using the ratio provided. Once Raju's age at marriage is found, use the constant age difference to find his sister's age at that time, and finally add 8 years to find her present age.
Step 3: Detailed Explanation:
Let Raju's present age be denoted as $R$.
The problem states he got married 8 years ago. So, Raju's age at the time of his marriage was $(R - 8)$.
We are given that his present age is $\frac{6}{5}$ times his age at the time of marriage. This gives us the equation:
\[ R = \frac{6}{5} \times (R - 8) \]
Multiply both sides by 5 to eliminate the fraction:
\[ 5R = 6(R - 8) \]
Expand the right side:
\[ 5R = 6R - 48 \]
Rearranging the terms, we get Raju's present age:
\[ R = 48 \text{ years} \]
This means Raju was $48 - 8 = 40$ years old at the time of his marriage.
The problem states Raju's sister was 10 years younger than him at the time of his marriage. Note that the age difference between two people remains constant throughout their lives.
Sister's age at the time of Raju's marriage = $40 - 10 = 30$ years.
We need to find the present age of Raju's sister. Since 8 years have passed since the marriage, we must add 8 to her age back then.
Sister's present age = $30 + 8 = 38$ years.
Step 4: Final Answer:
The present age of Raju's sister is 38 years.