Ravi’s Age Problem — Word to Equation
The Question
Ravi is 3 years older than Sita. The sum of their ages is 25 years. Find the age of each.
Why Age Problems Need Equations
We have two unknowns (Ravi’s age and Sita’s age), but we’re given two pieces of information. We use those two pieces to write one equation with one variable — and solve.
The skill here is translating the words into maths. This is the hardest part for most students. Let’s take it slow.
Step 1: Identify the Unknown
We have two ages to find. We need to choose one of them as our variable.
Let’s say: Let Sita’s age = x years.
Step 2: Express the Other Unknown in Terms of x
“Ravi is 3 years older than Sita.”
If Sita is x, then Ravi is x + 3.
So: Ravi’s age = (x + 3) years.
Step 3: Form the Equation
“The sum of their ages is 25.”
Sita’s age + Ravi’s age = 25
x + (x + 3) = 25
Step 4: Solve the Equation
x + x + 3 = 25
2x + 3 = 25
Transpose +3 to the right:
2x = 25 - 3
2x = 22
Transpose ×2 to the right:
x = 22 ÷ 2
x = 11
Step 5: Find Both Ages
Sita’s age = x = 11 years
Ravi’s age = x + 3 = 11 + 3 = 14 years
Step 6: Verify
“Ravi is 3 years older than Sita”: 14 - 11 = 3 ✓
“Sum of their ages is 25”: 11 + 14 = 25 ✓
Both conditions are satisfied. Our answer is correct.
Translating Key Phrases
One of the hardest things about word problems is turning English phrases into maths expressions. Here’s a handy reference:
| English Phrase | Maths Expression |
|---|---|
| ”a more than b” | b + a |
| ”a less than b” | b - a |
| ”3 times a number” | 3x |
| ”a number increased by 5” | x + 5 |
| ”a number decreased by 4” | x - 4 |
| ”sum of two numbers is 20” | x + y = 20 or x + (x+?) = 20 |
| ”twice a number” | 2x |
| ”half of a number” | x/2 |
When a word problem says “A is k more than B,” always set up as: A = B + k. The phrase “more than” means addition, and the reference person (B) gets the base value.
Common mistake: Writing Ravi’s age = 3x instead of x + 3.
“3 years older” means add 3, not multiply by 3. “3 times older” would mean multiply by 3.
Read carefully: “3 YEARS older” → +3. “3 TIMES older” → ×3.
Try These Similar Problems
Problem 1: Priya is 5 years younger than her brother. Together their ages add up to 27. Find their ages.
Let brother’s age = x. Priya’s age = x - 5 (5 years younger).
Sum: x + (x - 5) = 27 2x - 5 = 27 2x = 32 x = 16
Brother’s age = 16 years. Priya’s age = 16 - 5 = 11 years.
Verify: 16 + 11 = 27 ✓, and 16 - 11 = 5 ✓
Problem 2: A mother is 4 times her daughter’s age. The sum of their ages is 40. Find their ages.
Let daughter’s age = x. Mother’s age = 4x.
Sum: x + 4x = 40 5x = 40 x = 8
Daughter = 8 years. Mother = 4 × 8 = 32 years.
Verify: 8 + 32 = 40 ✓, and 32 = 4 × 8 ✓
Problem 3: Two years ago, Arjun’s age was 15. What is his age now?
Let Arjun’s current age = x. Two years ago: x - 2 = 15 x = 15 + 2 = 17 years
Arjun is 17 years old now.
Exam tip: Age problems are very popular in CBSE exams. The key steps examiners look for are: (1) defining the variable clearly (“Let Sita’s age = x”), (2) forming the equation, (3) solving correctly, (4) finding both quantities, (5) verification. Write all five steps for full marks.