The present ages of Pranay and Sai are in the ratio 15:17. After 6 years, the ratio of their ages will become 9:10. What will be the age of Pranay after 6 years from now?

Introduction / Context:
This question involves the present ages of two people, Pranay and Sai, expressed as a ratio. A different ratio is given for their ages after 6 years. Using these two ratios, we need to determine Pranay's age after 6 years. Such questions are typical in aptitude tests under problems on ages and ratios, combining basic algebra with proportional reasoning.

Given Data / Assumptions:
The present age ratio of Pranay to Sai is 15:17. After 6 years, the ratio of their ages will be 9:10. Ages are assumed to be in whole years. We must find Pranay's age after 6 years.

Concept / Approach:
When ages are given in a ratio, we can assign a common multiplier to convert the ratio into actual ages. If the present ratio is 15:17, we can write the ages as 15k and 17k. A future ratio condition is then expressed using these same expressions plus the number of years being added. Solving the resulting equation for k gives the actual ages.

Step-by-Step Solution:
Step 1: Let the present age of Pranay be 15k years and the present age of Sai be 17k years.Step 2: After 6 years, Pranay will be 15k + 6 years old and Sai will be 17k + 6 years old.Step 3: At that time, the ratio of their ages is given as 9:10, so (15k + 6) / (17k + 6) = 9 / 10.Step 4: Cross multiply: 10 * (15k + 6) = 9 * (17k + 6).Step 5: Expand both sides: 150k + 60 = 153k + 54.Step 6: Rearrange to get 150k + 60 - 153k - 54 = 0, which simplifies to -3k + 6 = 0, so 3k = 6 and k = 2.Step 7: Therefore, Pranay's present age is 15k = 30 years, and after 6 years he will be 30 + 6 = 36 years.

Verification / Alternative check:
With k = 2, Sai's present age is 17 * 2 = 34 years. After 6 years, Pranay will be 36 years old and Sai will be 40 years old. The ratio 36:40 simplifies to 9:10 when both numbers are divided by 4. This matches the ratio given in the question, confirming that the calculation is correct.

Why Other Options Are Wrong:
If Pranay were 42 years old after 6 years, his present age would be 36 years, and it would be impossible to maintain the required 15:17 current ratio and 9:10 future ratio simultaneously. Similarly, an age of 24 years after 6 years would mean a present age of 18 years, which does not fit these ratios. The option 30 years corresponds to Pranay's present age, not his age after 6 years, so it is not the required answer. Only 36 years satisfies all conditions.

Common Pitfalls:
Some learners mistakenly set up the ratio with incorrect future ages or forget to add 6 to both ages. Others confuse the present ratio with the future ratio or cancel terms incorrectly when cross multiplying. Always write the ratio equation carefully and solve step by step for the common multiplier k.

Final Answer:
Pranay will be 36 years old after 6 years.