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Introduction
Some age problems give information using conditions rather than direct ages. For example: "Rahul is twice as old as Neha" or "After 5 years, father will be 3 times the son’s age". These are called Conditional Statement age problems.
The key is to assign variables to unknown ages and convert each sentence into a clear equation. Once you do this, solving becomes straightforward.
Pattern: Conditional Statements in Age
The key idea:
Assign a variable to the unknown age (usually the youngest person).
Translate each sentence of the problem into a mathematical equation using the given condition.
Solve the resulting equation(s) to find the required age(s).
Step-by-Step Example
Question
Rahul is twice as old as Neha. After 5 years, he will be 3 years older than Neha. Find their present ages.
Options:
- A: Neha = 3 years, Rahul = 6 years
- B: Neha = 4 years, Rahul = 8 years
- C: Neha = 5 years, Rahul = 10 years
- D: Neha = 6 years, Rahul = 12 years
Solution
-
Step 1: Assign variables.
Let Neha’s present age = x.
Rahul’s present age = 2x (twice Neha). -
Step 2: Translate the future condition.
After 5 years:
Neha = x + 5
Rahul = 2x + 5
Condition: 2x + 5 = (x + 5) + 3 -
Step 3: Solve the equation.
2x + 5 = x + 8
x = 3 -
Step 4: Find actual ages.
Neha = 3 years
Rahul = 6 years -
Final Answer:
Neha = 3 years, Rahul = 6 years → Option A -
Quick Check:
After 5 years: Neha = 8, Rahul = 11 → difference = 3 years ✅
Quick Variations
Conditional statements can involve past ages, future ages, or multiples of ages. The process is always: assign variable → translate condition → solve equation.
Trick to Always Use
- Step 1: Assign variable to the unknown age.
- Step 2: Convert each condition into an equation.
- Step 3: Solve carefully.
- Step 4: Verify using the original condition.
Summary
- Identify the unknown(s) and assign variables.
- Translate conditional statements into equations accurately.
- Solve step-by-step to get the required ages.
- Verify by plugging values back into the condition.
Example to remember: Assign variable → Translate → Solve → Verify