Algebra basics

Story hook

"A father is 4 times as old as his son. After 20 years, he will be only twice as old. Find their present ages."

Brute-force approach: Try father = 30, son = 7.5 → no. Try 40, 10 → after 20 yrs, 60 vs 30. Yes! Coincidence? Or did you guess?

Algebraic approach (10 seconds): Let son = x. Father = 4x. After 20: father = 4x + 20; son = x + 20. 4x + 20 = 2(x + 20) → 4x + 20 = 2x + 40 → 2x = 20 → x = 10.

Algebra doesn't require luck. Every age problem, every "some-thing-times-something" word problem, becomes a one-equation, one-unknown affair.

CSAT loves age problems, sum-difference problems, and linear-equation-disguised-as-puzzle problems. After this unit, every such question is a 60-second template.

Why this matters for UPSC

For CSAT (Paper II, qualifying 33%):

• 6-9 questions per paper are pure algebra (linear or quadratic).
• Algebra is the universal solver — when number-system tricks fail, when alligation gets messy, set variables and write equations.
• Quadratic equations appear in 1-2 CSAT questions per year (max/min problems, "find a number such that…").
• Real-life: Budget planning, age/year calculations, monthly EMI computations.

The single most transferable maths skill for CSAT. Master linear equations and 70% of the qualifying paper becomes mechanical.