Problems on Ages

The Pro Approach: 90% of Age problems are just Ratio problems in disguise. Eliminate 'x' and use "Units".

The Logic: Time passes equally for everyone. So, the "Gap" between two people must remain constant.

• Step 1 (The Check): Look at the vertical gap in ratios.
• Step 2 (The Balance): If gaps differ, cross-multiply the horizontal differences to fix them.
• Step 3 (The Shot): 1 Unit Gap = Actual Years Passed. Boom.

Confusion Killer: "5 years ago" vs "10 years hence" can get messy. Stop doing mental gymnastics.

The Method: Draw a straight line.

Past (-5) <------ [ PRESENT (0) ] ------> Future (+10)

Always anchor your 'x' or 'Ratio' at the Present (T=0) unless the question forces otherwise.

The Speed Hack: Why solve complex quadratic equations when the answer is staring at you?

When to use: Complex multiplications, squares, or weird conditions.

How to do it:

• Divisibility Check: If A:B is 3:4, A's age MUST be a multiple of 3. Eliminate options that aren't.
• Plug & Play: Take limits. If Option A says 10, does condition match? If 10 is too small, skip to Option C.

Universal Truth: The age difference between two people is irrelevant to time.

(Age of A - Age of B) is ALWAYS Constant.

If your father is 25 years older than you today, he was 25 years older when you were born, and he will be 25 years older when you retire.

Examiners set traps in English/Hindi. Decode them:

• A is 3 times B → Ratio 3:1
• A is 3 times MORE than B → A = B + 3B → Ratio 4:1
• A is 150% of B → Ratio 3:2

Myth: "If average age increases by 1 year, everyone's age increases by 1 year."

Reality: Total Age increases by 1 × N.

If a 60yo leaves and a new person comes, and avg decreases by 2 (for 10 ppl):

New = 60 - (2 × 10) = 40. (The Replacement Rule applies here too!)