The ratio of the present age of Yuvaraj to the present age of Ganguly is 4 : 3. Yuvaraj will be 26 years old after 6 years. What is the present age of Ganguly?

Introduction / Context:
This age problem combines a present age ratio with information about the future age of one person. The task is to determine the current age of the second person. It checks your ability to handle ratios and to move forward or backward in time when working with ages.

Given Data / Assumptions:

• Present age ratio of Yuvaraj to Ganguly is 4 : 3.
• Yuvaraj will be 26 years old after 6 years.
• We need the present age of Ganguly.
• All ages are expressed in years and are positive.

Concept / Approach:
When a future age is given, we subtract the time difference to find the current age. Using the ratio, we then express both ages in terms of a common variable and match it to the known current age of one person. This directly gives the variable and the age of the other person.

Step-by-Step Solution:
Let present age of Yuvaraj be 4 * x years.Let present age of Ganguly be 3 * x years.We know that after 6 years, Yuvaraj will be 26 years old.So 4 * x + 6 = 26.Rearrange: 4 * x = 26 - 6 = 20.Therefore x = 20 / 4 = 5.Present age of Yuvaraj = 4 * 5 = 20 years.Present age of Ganguly = 3 * 5 = 15 years.

Verification / Alternative check:
Check future age: After 6 years, Yuvaraj age will be 20 + 6 = 26 years, which matches the given statement.Check the present ratio: 20 : 15 simplifies to 4 : 3 by dividing both numbers by 5.Hence the solution for Ganguly age as 15 years is consistent with both pieces of information.

Why Other Options Are Wrong:
17 years: This would correspond to a ratio that does not match 4 : 3 when paired with Yuvaraj correct age.19 years: This is too large and cannot maintain the 4 : 3 ratio given the future condition.12 years: This is too small and also fails to maintain the correct ratio and future information.

Common Pitfalls:
Some students mistakenly set 4 * x equal to 26 instead of 4 * x + 6, forgetting the 6 years to be added.Others misinterpret the ratio and use 3 : 4 rather than 4 : 3, which reverses the roles of Yuvaraj and Ganguly.Mixing present and future values without adjusting correctly often leads to wrong equations.

Final Answer:
The present age of Ganguly is 15 years.