Average

Story hook

It is the CSAT 2023 exam hall. A candidate sees:

"A vessel contains 60 litres of milk. 12 litres of milk is drawn and replaced with water. This is repeated twice more. What is the final ratio of milk to water?"

She tries to track it step-by-step. After 4 minutes, she's muddled the arithmetic and skips it.

The candidate next to her uses one formula:

Final milk fraction = (1 - 12/60)^3 = (0.8)^3 = 0.512 → Milk : Water = 0.512 : 0.488 ≈ 64 : 61 (or close).

30 seconds. Done.

Average + Alligation + Mixtures = the trio of "comparison- shortcut" topics. Used in 8-12 questions every CSAT paper. The shortcuts here aren't just speed-ups — they're the difference between solving in 30 seconds and not solving at all.

Why this matters for UPSC

For CSAT (Paper II, qualifying 33%):

• 8-12 questions per paper touch averages, mixtures, or alligation: mean of N students, runs scored across innings, alligation of two grades of rice, replacement problems.
• The same alligation formula is reused in Profit-and-Loss (cost mixing), in Speed-Distance (average speed for two halves of journey), and even in Time-and-Work (combining different worker speeds).
• Average is the simplest formula in maths; getting it wrong is a candidate's biggest unforced error.

Average + Alligation = second-highest yielding topic in CSAT prep after Percentages. ~3 hours of practice = ~10% of paper.