Question
Ravi is 4 years older than Priya. Five years ago, Ravi was three times as old as Priya. Find their present ages.
Solution — Step by Step
Let Priya’s present age = years.
Then Ravi’s present age = years (since Ravi is 4 years older).
“Five years ago, Ravi was three times as old as Priya.”
Five years ago: Priya = , Ravi =
Condition:
Priya = 7 years, Ravi = 11 years.
Verification: Five years ago, Priya was 2 and Ravi was 6. Is 6 = 3 times 2? Yes ✓
Why This Works
graph TD
A["Word Problem Solving Algorithm"] --> B["Step 1: Read twice, identify what is asked"]
B --> C["Step 2: Assign variables to unknowns"]
C --> D["Step 3: Translate each condition to an equation"]
D --> E["Step 4: Solve the equation"]
E --> F["Step 5: VERIFY by substituting back into the original words"]
F --> G["Does the answer make sense? Positive ages? Logical?"]The key skill is translation — converting English sentences into mathematical equations. Here is a phrase-to-math dictionary:
| English Phrase | Mathematical Translation |
|---|---|
| ”is” / “was” / “will be" | |
| "more than” / “older than" | |
| "less than” / “younger than" | |
| "times” / “of" | |
| "sum of A and B" | |
| "product of A and B" | |
| "years ago” | subtract from current |
| ”years hence” | add to current |
The verification step is not optional — it catches sign errors and misinterpretations. It takes 30 seconds and can save you from losing full marks.
Alternative Method
For age problems, a quick sanity check: the age difference between two people never changes. If Ravi is 4 years older now, he was 4 years older five years ago, and he will be 4 years older ten years from now. This constraint often helps eliminate wrong options in MCQs.
For problems with more than two people, set up simultaneous equations. Use the youngest person’s age as the base variable — this usually keeps numbers positive.
Common Mistake
Setting up the equation backwards. “Ravi was three times as old as Priya” means , NOT . Students often reverse the multiplier. A quick check: Ravi is older, so his age should be the larger number. If your equation makes the younger person 3 times the older, something is wrong.