Raju got married 8 years ago. His present age is six fifths of his age at the time of marriage. Raju sister was 10 years younger than him at the time of his marriage. What is the present age of Raju sister?

Introduction / Context:
This problem involves age relationships at the time of marriage and in the present. Raju present age is given as a fraction of his age at marriage, and his sister age is related to his age at that same time. The question finally asks for the sister present age, a common format in problems on ages.

Given Data / Assumptions:

• Raju got married 8 years ago.
• His present age is six fifths of his age at the time of marriage.
• At the time of marriage, Raju sister was 10 years younger than him.
• We must find the present age of Raju sister.
• All ages are in years and positive.

Concept / Approach:
We first calculate Raju age at the time of marriage by introducing a variable for that age. Using the fractional relationship, we convert to his present age. Once Raju age at marriage is known, we subtract 10 years to get his sister age at marriage. Finally, we add 8 years to find the sister present age. The approach uses stepwise reasoning across time points.

Step-by-Step Solution:
Let Raju age at the time of marriage be M years.Eight years have passed since his marriage, so his present age is M + 8 years.We are told that his present age is six fifths of his age at marriage.So M + 8 = (6 / 5) * M.Multiply both sides by 5 to clear the fraction: 5 * (M + 8) = 6 * M.This gives 5 * M + 40 = 6 * M.Rearrange: 40 = 6 * M - 5 * M = M.So Raju age at marriage was 40 years.His present age is M + 8 = 40 + 8 = 48 years.Raju sister was 10 years younger than him at the time of marriage, so her age then was 40 - 10 = 30 years.Since 8 years have passed, her present age is 30 + 8 = 38 years.

Verification / Alternative check:
Raju at marriage: 40 years, sister at marriage: 30 years.Present ages: Raju = 48 years, sister = 38 years.Check the fractional relationship: six fifths of 40 is (6 / 5) * 40 = 48, which matches Raju present age.Check the age difference between Raju and his sister: 40 - 30 = 10 years at marriage and 48 - 38 = 10 years now, consistent across time.

Why Other Options Are Wrong:
30 years: This is the sister age at the time of Raju marriage, not her present age.32 years: This does not maintain the 10-year age difference with the correctly computed present age of Raju.None of these: This is incorrect because 38 years is a valid option and satisfies all the conditions.

Common Pitfalls:
Learners sometimes misinterpret the fraction and write present age as five sixths of the marriage age instead of six fifths.Another mistake is to forget that 8 years have also passed for the sister, leading them to give her age at marriage rather than her present age.Errors in solving M + 8 = (6 / 5) * M can lead to a wrong value of M.

Final Answer:
The present age of Raju sister is 38 years.