Time, Speed and Work
CSAT time, speed, distance and work for UPSC Prelims Paper II — average and relative speed, trains, boats and streams, work efficiency, pipes and man-days.
SyllabusCSAT · Basic numeracy (numbers and their relations, orders of magnitude, etc.) — Class X level
Time–speed–distance and time–work questions are a dependable part of CSAT’s basic numeracy. They share one structure: a rate multiplied by time gives an amount — kilometres covered, or work done. Once you see that, trains, boats, pipes and workers are the same problem in different costumes.
This chapter is Prelims-only. The aim is not to memorise dozens of formulas but to master three ideas — unit conversion, relative speed and the total-work (LCM) method — and apply them in under two minutes per question.
What this chapter covers
| Sub-topic | Core idea |
|---|---|
| Speed, distance, time | $D = S \times T$; km/h ↔ m/s |
| Average speed | Total distance ÷ total time; $\dfrac{2xy}{x+y}$ for equal distances |
| Relative speed | Add for opposite directions, subtract for the same direction |
| Trains, boats and streams | Lengths add when crossing; downstream $b + s$, upstream $b - s$ |
| Time and work | Total work = LCM of days; efficiency = work per day |
| Pipes and man-days | Emptying pipes do negative work; $M_1 D_1 H_1 = M_2 D_2 H_2$ |
Start with Time, Speed, Distance and Work, revise with the quick-revision sheet and practise on the question set.