Problems on Ages is a crucial topic for all competitive exams. Understanding the basics helps you solve problems quickly and accurately.
Key Formulas
Key Formula
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⚡ Shortcut Tricks
#1
One variable method: If father is twice son's age NOW, assume son = x, father = 2x. Then apply future/past conditions.
#2
Ratio + common factor x: If ages are in ratio 4:3 five years ago and 5:4 two years hence — difference between years = 7, difference in ratio = 1, so x = 7/1 = 7.
#3
Sum and product method: If sum = S and product = P, form equation x² - Sx + P = 0 and solve using quadratic formula.
#4
Simultaneous equations: Always form 2 equations for 2 unknowns — one from present condition, one from past/future condition.
#5
Key translation: 'x years ago' means SUBTRACT x. 'x years hence' means ADD x. 'x times as old' means MULTIPLY.
#6
Sum of ages always increases by (number of people × years passed). If 2 people, after 5 years sum increases by 10.