Time & work

Story hook

"A can paint a wall in 6 days, B in 8 days. Together?"

Average it: (6+8)/2 = 7 days? Wrong.

Take LCM: LCM(6, 8) = 24. Total work = 24 units. A does 24/6 = 4 units/day. B does 24/8 = 3 units/day. Together = 7 units/day. Time = 24/7 = 3.43 days.

Faster than either alone. The combined rate is the sum of individual rates, NOT the average of times.

This is the single most common conceptual trap in Time and Work — and it appears in 3-5 questions per CSAT paper. After this unit, every work-problem becomes a 60-second "compute units" exercise.

Pipes & cisterns are mathematically identical — "filling pipe" = positive worker, "drain pipe" = negative worker.

Why this matters for UPSC

For CSAT (Paper II, qualifying 33%):

• 5-7 questions per paper on Time and Work or Pipes-Cisterns.
• The LCM trick (rather than fraction-juggling) is the defining skill — saves 30-60 seconds per problem.
• Real applications: Estimating project completion times (combining team capacities); calculating effective bandwidth on shared internet; reservoir filling/draining (water management).

This unit unlocks ~6-8% of CSAT marks. Two hours of focused practice will pay off the entire investment.