SSC CGL Time & Work and Time-Speed-Distance Notes: Formulas & Practice

Time & work and time-speed-distance are the two most dependable chapters in SSC CGL Quant. They never change format: efficiency-based work questions, relative-speed meetings, train crossings and boats-and-streams appear in almost every shift with only the numbers swapped. A handful of methods covers everything.

Both chapters share one idea — a rate. In time & work the rate is efficiency (work per day); in time-speed-distance the rate is speed (distance per hour). Once you think in rates, 'A and B together', 'trains crossing' and 'boat upstream' all become the same kind of calculation.

This chapter covers the efficiency method for work, pipes and cisterns, the speed-distance-time triangle, relative speed, train-length rules, and boats and streams — with the unit traps that SSC plants in every one of them.

Key Concepts & Formulas

Time & work — the efficiency method

Time-and-work questions are about efficiency, not time. If A finishes a job in 12 days, A does 1/12 of the job per day; if B takes 15 days, B does 1/15 per day. Working together they do (1/12 + 1/15) per day, so the job takes 1/(1/12 + 1/15) days. The LCM trick makes this instant: total work = LCM of the days (60), A's efficiency = 60/12 = 5, B's = 60/15 = 4, together = 60/9 = 6 and 2/3 days.

Formulas:

• Efficiency = 1 / (days taken by one person)
• Days together = Total work / (sum of efficiencies)
• Total work = LCM of individual days; efficiency = LCM / days

Pipes and cisterns — work with a minus sign

Pipes and cisterns are time-and-work with water. A filling pipe is a worker doing positive work; an emptying pipe is a worker doing negative work (undoing the job). If pipe A fills in 6 hours (efficiency +1/6) and leak B empties in 12 hours (efficiency -1/12), together they fill (1/6 - 1/12) = 1/12 per hour — 12 hours to fill. The only new habit is the minus sign.

Formulas:

• Filling pipe: +1/(hours to fill); Emptying pipe or leak: -1/(hours to empty)
• Net rate = sum of signed efficiencies; Time = 1 / net rate

Speed, distance, time — the core formula

Speed is distance divided by time, and the formula triangle keeps the three versions straight: cover up the one you need and read off what remains. The unit conversion is the exam-setter's favourite trap: 1 km/h = 5/18 m/s and 1 m/s = 18/5 km/h. A speed of 72 km/h becomes 72 x 5/18 = 20 m/s — a calculation worth practising until it is automatic.

Formulas:

• Speed = Distance / Time; Distance = Speed x Time; Time = Distance / Speed
• 1 km/h = 5/18 m/s; 1 m/s = 18/5 km/h

Relative speed — same vs opposite direction

Relative speed replaces two moving objects with one: for objects moving TOWARDS each other (opposite directions) the closing speed is the SUM of their speeds; for objects moving the SAME direction (a chase) it is the DIFFERENCE. A faster train crossing a slower train from behind closes at (fast - slow). Get same/opposite backwards and the answer will be one of the wrong options.

Formulas:

• Opposite directions: relative speed = speed1 + speed2
• Same direction: relative speed = |speed1 - speed2|
• Meeting time = distance between them / relative speed

Trains — when to add the lengths

Train questions are relative-speed questions in disguise, with one extra rule: when a train crosses anything WITH length (another train, a platform, a bridge), the distance covered is the SUM of the lengths. When it crosses a point with NO length (a pole, a person standing still), the distance is just the train's own length. The exam's favourite trap is giving a platform length and watching people forget to add it.

Formulas:

• Crossing a pole/person: distance = length of train
• Crossing a platform/bridge/train: distance = length of train + length of the other
• Time = total distance / speed (convert units first!)

Boats and streams

Still-water speed is the boat's own engine; the stream helps downstream and fights upstream. Downstream speed = boat + stream, upstream speed = boat - stream. Two useful consequences: the stream's speed is half the difference of downstream and upstream speeds, and average round-trip speed for a fixed distance is NOT the average of the two speeds — it is 2xy/(x+y).

Formulas:

• Downstream speed = boat speed + stream speed
• Upstream speed = boat speed - stream speed
• Stream speed = (downstream - upstream)/2; Boat speed = (downstream + upstream)/2

Solved Examples

Practice Questions

Common Traps (galtiyan jo marks katwati hain)

• Unit mismatch: train speeds come in km/h while lengths are in metres. Convert to m/s with x 5/18 BEFORE dividing — solving in km/h and converting at the end is where errors creep in.
• Train length rule: crossing a platform or bridge means distance = train length + platform length. Forgetting to add the platform is SSC's favourite train trap.
• Same vs opposite direction: opposite directions ADD speeds; same direction SUBTRACTS. 'Overtakes' means same direction (difference) — misreading it flips the answer.
• Average speed: for a round trip over the same distance, average speed = 2xy/(x+y), never (x+y)/2. The slower leg takes more time, so it drags the average down.
• Pipe signs: an emptying pipe or leak is NEGATIVE work. A question with 'a leak empties in 12 hours' that you treat as positive will give you a filling time faster than either pipe alone — physically impossible.
• Man-days confusion: '8 men in 12 days' means total work = 8 x 12 man-days. Doubling the men halves the days only when the total work stays fixed — check the question hasn't also changed the job.

FAQs