Question
Rahul’s age is 3 times Riya’s age. 5 years ago, Rahul’s age was 5 times Riya’s age. Find their present ages.
Solution — Step by Step
Let Riya’s present age = years.
Then Rahul’s present age = years (given: Rahul’s age is 3 times Riya’s).
Five years ago:
- Riya’s age =
- Rahul’s age =
Five years ago, Rahul’s age was 5 times Riya’s age:
Riya’s present age = years
Rahul’s present age = years
Verification:
- Present: Rahul (30) = 3 × Riya (10) ✓
- Five years ago: Rahul (25) = 5 × Riya (5) ✓
Why This Works
Age problems always involve a constant difference: a person who is 20 years older today was also exactly 20 years older 5 years ago. The RATIO changes over time, but the DIFFERENCE stays the same.
Here, Rahul is years older than Riya. When Riya is 10 and Rahul is 30, the difference is 20 years. When Riya was 5 and Rahul was 25, the difference was still 20 years. That constant gap is what makes these equations solvable.
Alternative Method — Working Backwards
If Rahul’s age was 5 times Riya’s five years ago, and now it’s 3 times: as Riya got older, the ratio decreased. Let Riya be years old five years ago. Then Rahul was years old.
Present ages: Riya = , Rahul = .
Condition now:
So Riya was 5 five years ago, making her 10 now. Same answer.
Common Mistake
The most common error is setting up the “5 years ago” equation as: (present age of Rahul) = 5 × (present age of Riya − 5), mixing past time with present age. Both ages must be at the same point in time. If you’re working 5 years ago, subtract 5 from BOTH ages: . Not — this would mix present Rahul age with past Riya age.