Averages , Ratio and Proportion Question 3 - CAT 2024
When Rajesh’s age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima’s age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become:
Step-by-Step Explanation
Let the present ages of Rajesh and Garima be R and G. The difference between their ages remains constant over time. Let this age gap be x:
R − G = x ⟹ R = G + x
- Analyze the past state:
When Rajesh was Garima's current age (G), it was exactly x years ago. At that time, Garima's age was G − x.
G/(G − x) = 3/2 ⟹ 2G = 3G − 3x ⟹ G = 3x
Since G = 3x, Rajesh's present age is:
R = 3x + x = 4x
- Analyze the future state:
When Garima reaches Rajesh's current age (4x), it will be exactly x years in the future. At that time, Rajesh's age will be:
R + x = 4x + x = 5x
Future Ratio (Rajesh : Garima) = 5x : 4x = 5 : 4
Correct Option: C
💡 FundaMakers Tip:
Age gaps are absolute invariants across time. Setting the constant age difference as x allows you to express their past, present, and future timelines cleanly in terms of a single base factor (x), avoiding complex simultaneous systems.