Time and Work, Speed and Distance
Time and Work, Speed and Distance
These two chapters share one structure — work per unit time and distance per unit time — so one method covers both. Together they contribute 2 to 3 questions in the Part-III paper, including pipes, trains and boats, which do not appear at Part-II level.
Time and Work by the LCM Method
Take the total work as the LCM of the given days. Each worker then has a whole-number rate, and fractions disappear.
A takes 10 days, B takes 15, C takes 30. LCM is 30 units. Rates are 3, 2 and 1 unit a day, total 6, so together they finish in 5 days.
Two workers: combined time = (a × b) ÷ (a + b)
- Efficiency and time are inversely proportional: twice as efficient means half the time.
- If A is 50 per cent more efficient than B, their time ratio is 2 : 3.
- For alternate-day work, compute a two-day block and count how many blocks fit.
- Negative work is the key to leaving-mid-way problems: subtract the departed worker's share.
Pipes and Cisterns
Identical to work, with one change of sign. An inlet does positive work, an outlet does negative work.
A pipe fills a tank in 6 hours, another empties it in 8. Together, taking 24 units, the rates are +4 and −3, so the net is +1 and the tank fills in 24 hours.
✗ An inlet of 6 hours and outlet of 8 hours together fill in 48/14 hours | ✓ Rates subtract, not add: 4 − 3 = 1 unit per hour, so 24 hours
Speed, Time and Distance
Distance = Speed × Time | km/h to m/s: multiply by 5/18
Average speed for equal distances = 2xy ÷ (x + y)
For the same distance, time is inversely proportional to speed, so speeds in the ratio 3 : 4 mean times in the ratio 4 : 3. That single line solves most of the harder questions without any formula at all.
✗ Travelling out at 40 and back at 60, the average speed is 50 km/h | ✓ It is 2 × 40 × 60 ÷ 100 = 48 km/h
Trains and Boats
| Situation | Distance or speed to use |
|---|---|
| Train crossing a pole | Length of the train |
| Train crossing a platform | Train length + platform length |
| Two trains, same direction | Relative speed = difference |
| Two trains, opposite directions | Relative speed = sum |
| Boat downstream | Boat speed + stream speed |
| Boat upstream | Boat speed − stream speed |
Boat speed = (downstream + upstream) ÷ 2 | Stream speed = (downstream − upstream) ÷ 2
Those two boat formulas are asked directly and take ten seconds once memorised. For trains, the commonest error is forgetting that a train crossing a platform must cover its own length as well.
समान दूरी पर समय चाल के व्युत्क्रमानुपाती होता है।
TRE pointer: Pipes and cisterns is the topic that most clearly marks a Part-III paper apart from a Part-II one, and the sign of the outlet is where candidates slip. The average-speed trap — taking the plain mean instead of 2xy/(x+y) — is repeated year after year, with the wrong value sitting among the options. Since these questions are all verifiable by substitution, they are poor candidates for option E and good candidates for careful attempt.
60-Second Recap
- Use the LCM method: total work = LCM of the days, then work in whole-number rates.
- Efficiency and time are inversely proportional.
- In pipes and cisterns, outlets have negative rates, so they subtract.
- km/h to m/s is × 5/18; for a fixed distance, time is inversely proportional to speed.
- Average speed over equal distances is 2xy/(x+y), never the plain mean.
- Boat speed = (down + up)/2; stream speed = (down − up)/2.
Frequently Asked Questions
Why use the LCM method for time and work?
Because it removes fractions entirely. Taking the total work as the LCM of the individual times gives every worker a whole-number rate per day, so combining, subtracting and comparing workers becomes simple arithmetic. It is far less error-prone than adding fractions under time pressure.
How do I handle an outlet pipe?
Give it a negative rate and add it to the inlet rates. If an inlet contributes four units an hour and an outlet removes three, the net is one unit an hour. Adding the two rates as if both were filling is the standard mistake in this topic.
What is the average speed if I go at 40 and return at 60?
Forty-eight kilometres an hour, from two xy divided by x plus y. It is not fifty, because more time is spent at the slower speed, which pulls the average down. The plain mean is always placed among the options as the obvious wrong answer.
How do I find boat and stream speeds?
The boat's speed in still water is the average of the downstream and upstream speeds, and the stream's speed is half their difference. Both follow from downstream being boat plus stream and upstream being boat minus stream, and both are asked directly.
Next step: Arithmetic is decided by which traps you have already met. Meet them in the BPSC TRE 4.0 mock test on ExamAtlas — five options, −1/3 negative marking, and the Part-III depth this chapter prepares you for.