The ages of Krish and Vaibhav are in the ratio 3 : 5 at present. After 9 years, the ratio of their ages will become 3 : 4. What is the current age of Vaibhav in years?

Introduction / Context:
This question is about age ratios that change over time. It tests your ability to translate ratio information into algebraic expressions and use future conditions to find the actual ages. Such problems are very common in quantitative aptitude exams.

Given Data / Assumptions:

• Present ratio of the ages of Krish and Vaibhav is 3 : 5.
• After 9 years, the ratio of their ages will be 3 : 4.
• We need to find the current age of Vaibhav.
• All ages are in years and assumed to be positive integers.

Concept / Approach:
When an age ratio is given, we usually represent the actual ages as multiples of a common variable. Then, when we are told about a ratio at a future time, we translate that into another equation and solve for the variable. Once the value of the variable is known, we can compute the individual ages. This approach is systematic and avoids guesswork.

Step-by-Step Solution:
Let the present age of Krish be 3 * x years.Let the present age of Vaibhav be 5 * x years.After 9 years, Krish age will be 3 * x + 9, and Vaibhav age will be 5 * x + 9.The ratio after 9 years is given as 3 : 4, so (3 * x + 9) / (5 * x + 9) = 3 / 4.Cross-multiply to remove the fraction: 4 * (3 * x + 9) = 3 * (5 * x + 9).Simplify left side: 12 * x + 36.Simplify right side: 15 * x + 27.Set them equal: 12 * x + 36 = 15 * x + 27.Rearrange: 36 - 27 = 15 * x - 12 * x, so 9 = 3 * x.Therefore x = 3.Present age of Vaibhav = 5 * x = 5 * 3 = 15 years.

Verification / Alternative check:
Krish current age = 3 * 3 = 9 years, Vaibhav current age = 15 years.After 9 years: Krish will be 18, Vaibhav will be 24.Check ratio: 18 : 24 simplifies to 3 : 4 by dividing both terms by 6.The future ratio condition is perfectly satisfied, confirming that Vaibhav current age is 15 years.

Why Other Options Are Wrong:
10 years: Using this as Vaibhav age would break the 3 : 5 ratio between Krish and Vaibhav and will not satisfy the future ratio condition.13 years: This does not maintain the required future ratio of 3 : 4 after 9 years.18 years: This also fails either the present ratio or the future ratio condition or both.

Common Pitfalls:
Students sometimes confuse the ratios and incorrectly use the same ratio at both times without shifting ages by the number of years.Another mistake is to forget to add 9 years to both ages when forming the future ratio equation.Careless arithmetic in cross-multiplication can also lead to wrong values of x.

Final Answer:
The current age of Vaibhav is 15 years.