In one line: CSAT Part 5: After percentages and ratios (Part 3), the highest yield quant family is the trio of time-work, speed distance and trains — CSAT draws a.

In fact, after percentages and ratios (Part 3), the highest yield quant family is the trio of time-work. Meanwhile, speed distance and trains — CSAT draws a steady 4–8 questions from it every year. All three topics become trivial once you adopt one habit: work in units per minute and LCM-based “total work” , never in fractions of abstract rates.

Quick Answer: After percentages and ratios (Part 3), the highest yield quant family is the trio of time-work. Moreover, speed distance and trains — CSAT draws a steady 4–8 questions from it every year. Meanwhile, all three topics become trivial once you adopt one habit: work in units per minute and LCM-based “total work”, never in fractions of abstract…

Table of Contents

1. Therefore, time and Work: The LCM Method
2. Meanwhile, pipes and Cisterns: The Same Engine
3. Speed-Distance-Time: The Structure
4. As a result, relative Speed: The Concept That Runs Trains, Boats and Escalators
5. Trains: The Four Standard Wrappers
6. Boats, Streams and Average-Speed Traps
7. How Exams Probe This Topic
8. Quick Revision: One-Glance Facts

1. Time and Work: The LCM Method

• The core idea. In other words, assume total work = LCM of the given days . If A takes 12 days and B takes 18 days, take work = 36 units → A does 3 units/day. Therefore, b does 2 units/day ; together 5 units/day → 36/5 = 7.2 days . No fractions, no formulas.
• Notably, “A is twice as efficient as B” → A’s days = half of B’s. If the ratio of efficiencies is given (3:2), times run inverse (2:3).
• Standard wrappers.
• Indeed, alternating work: A and B alternate days — compute two-day blocks (5 units above), then finish the remainder with whoever’s turn it is.
• Specifically, mid-way leaving/joining: compute work done before the event, then solve the remainder with the new crew.
• Similarly, men days (M₁D₁H₁/W₁ = M₂D₂H₂/W₂): workforce scaling — the proportion form is faster than memorising derivations.
• Overall, wages: wages divide in the ratio of work done (efficiency ×days), not days alone.

2. Pipes and Cisterns: The Same Engine

• Consequently, inlet pipes are workers; the outlet/leak is negative work . Indeed, fill 12 h, drain 18 h, LCM = 36 → +3 − 2 = +1 unit/h → 36 hours.
• Furthermore, the leak fraction line: “a leak empties the filled tank in X hours. Meanwhile, pipe fills in Y — net time”: identical arithmetic, negative efficiency.
• Likewise, sequential opening: “A open for 2 hours, then B joins” — compute in two phases; never average rates blindly.

3. Speed-Distance-Time: The Structure

• The invariant discipline. In short, in multi-leg problems, hold the invariant quantity (same distance, same time. Meanwhile, or same speed) and write proportions: same distance → S₁/S₂ = T₂/T₁; same time → D ∝ S.
• Percentage change shortcuts. Subsequently, speed ↑20% → time ↓16.67% (×5/6, since ×6/5 on speed); the multiplier logic from Part 3 does the work.
• In fact, average speed = total distance / total time — never the arithmetic mean of speeds. Equal distances → harmonic mean: 2ab/(a+b). Going 30 and returning at 60 → average 40, not 45 — the single most tested trap.
• If D fixed, S×T constant (inverse); if S fixed, D∝T. Moreover, learn to spot the fixed quantity in the first read.

4. Relative Speed: The Concept That Runs Trains, Boats and Escalators

• Therefore, same direction: relative speed = difference . Opposite directions: relative speed = sum . Everything in sections 4–6 is this one-line applied.
• Meanwhile, time = (length to be covered) —relative speed. The “length to be covered” is the sum of lengths when two trains pass each other. The train’s own length when passing a pole/man (a man’s length is zero — that’s the whole trick).

5. Trains: The Four Standard Wrappers

1. As a result, train past a pole/man: T = train length —speed.
2. In other words, train past a platform/bridge/tunnel: T = (train + platform length) —speed.
3. Notably, two trains crossing (opposite): T = (L₁+L₂) —(S₁+S₂).
4. Two trains crossing (same-direction): T = (L₁+L₂) —(S₁−S₂). The faster must start behind — read who overtakes whom.

• km/h ↔ m/s: multiply by 5/18 (down), 18/5 (up). Most train errors are unit errors — convert before anything else.
• Two station meeting problems. Meeting time = distance —(S₁+S₂); each train’s share of distance is proportional to its speed — solve with ratio scaling, not simultaneous equations.

6. Boats, Streams and Average-Speed Traps

• Downstream speed = b + s; upstream = b − s; boat speed = (down + up)/2. Stream = (down − up)/2 — half-sum/half difference is the exam shortcut.
• Escalators (rare but appear in CSAT-style banks): steps visible + steps climbed vs escalator’s own rate — treat exactly like boats: person speed ± escalator-speed.
• The trap register. (a) average speed arithmetic mean error; (b) forgetting to add train length on platforms; (c) using km/h against metres in the same line; (d) same-direction relative speed taken as sum; (e) “rest time” included in average speed computations — exclude stops only when the question’s average is over travel time, include when over total time.

7. How Exams Probe This Topic

• The CSAT record: 2014–2025 papers reliably carry 1–2 time work questions (often the leaving midway wrapper), 1–2 trains/relative-speed, 1 average speed trap. A pipes or boat item — 4–8 marks on methods fully specified above.
• The drill: 25 questions (mixed across the five wrappers) in 25 minutes, 90% accuracy. Log every miss against the trap register (section 6) — the register is the revision sheet.
• Companion exams: CDS/CAPF and banking PO quant reuse identical wrappers at speed — one preparation serves three papers (see the Banking series, Part 4).

8. Quick Revision: One-Glance Facts

• Total work = LCM of days; rates become integers; wages split by work done.
• Outlet = negative efficiency; phases, never averages.
• Average = D/T only; equal distances → 2ab/(a+b).
• Sum (opposite), difference (same); crossing length = L₁+L₂ (or L+platform).
• ×5/18 km/h → m/s before any computation.
• mean-speed, pole-vs platform length, unit mix, direction sign, rest time wording.

This trio of topics is pure method: LCM for work, invariants for speed, sum and difference for relative motion. Convert units first, name the wrapper second. Apply the one-line rule third — and the 4–8 marks this family contributes each year become the most predictable quant marks on your CSAT scorecard.

Ten Worked Items (The Trio’s Full-Range)

1. A and B-do-a job-in-12-and-18-days; A-leaves-4-days before the end → total = ~13.1 days (the work-6-units/day-of LCM-36; B-alone-4-days = 24-units; the remaining-72-24=48? — hold the worked-honesty: the 36-units-total, the A+B-rate-5, the B-alone’s last-4 = 4-units → the together phase = 32÷5 = 6.4 → 10.4 days ).
2. Pipes-A and B-fill-in-20-and-30-min; C-empties-in-60 → all open: the tank-fills in 10 minutes (3+2−1 = 4-of LCM-60).
3. A-train-crosses-a-300-m-bridge-in-25-s-at-72-km/h → the train’s length = 200 m (20×25 − 300).
4. Walking-at-4/5-of his-speed, a man-is-10-minutes late → his-usual time = 40 minutes (the time-ratio-5:4’s inverse).
5. A-boat-covers-24-km-downstream-in-3-h-and returns-in-6-h → the stream = 2 km/h (the half-difference-of-8-and-4).
6. Two-trains-start-simultaneously-from A and B-300-km-apart-toward-each-other-at-60-and-40 → they meet in 3 hours (300÷100) at 180 km-from A (the distance-proportional-to speed).
7. A-can-do-a work-in-10-days; B-is-50%-more efficient → B-alone = 6.67 days (the efficiency-inverse).
8. the milk-and water-40-L-mixture (4:1) — 10-L-removed-and replaced twice → the milk’s fraction = (3/4)² = 56.25% .
9. A-car covers the first-half-at-40 and the second-half-at-60 → the average speed = 48 km/h (the harmonic-2ab/(a+b) — never-50).
10. 5-men-or-8-women-do-a job → 3-men-and-4-women take = the LCM-40: the man-8, the woman-5 → the rate-44 → ~9.1 days . Ten-items spanning the leaving midway (1), the pipes (2), the S-D-family (3, 4, 5, 6, 9), the efficiency inverse (7). The replacement (8) and the men-women equivalence (10) — the section’s whole-surface-in one-drill.

The Common-Wrong-Answers’ Ledger (Where-Marks-Die)

the average-speed’s arithmetic mean (the harmonic’s-26%-error). The “50%-more efficient = 50%-less-time” (the inverse’s error). The pole versus the bridge (the length-addition’s omission). The direction forgetting (the relative-speed’s sum-taken for the same-direction). The replacement’s whole-mixture-formula-applied to the milk only (the component not the solution-survives). And the units’ day-one discipline (the 5/18-conversion-before anything). Six-errors, six corrections — the ledger-reviewed-before every mock.

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Frequently Asked Questions

What should you know about 1. Time and Work: The LCM Method?

The core idea. Assume total work = LCM of the given days . If A takes 12 days and B takes 18 days, take work = 36 units → A does 3 units/day. B does 2 units/day ; together 5 units/day → 36/5 = 7.2 days . No fractions, no formulas. “A is twice as efficient as B” → A’s days = half of B’s. If the ratio of efficiencies is given (3:2), times run inverse (2:3).

What should you know about 2. Pipes and Cisterns: The Same Engine?

Inlet pipes are workers; the outlet/leak is negative work . Fill 12 h, drain 18 h, LCM = 36 → +3 − 2 = +1 unit/h → 36 hours. The leak fraction line: “a leak empties the filled tank in X hours. Pipe fills in Y — net time”: identical arithmetic, negative efficiency.

What should you know about 3. Speed-Distance-Time: The Structure?

The invariant discipline. In multi-leg problems, hold the invariant quantity (same distance, same time. Or same speed) and write proportions: same distance → S₁/S₂ = T₂/T₁; same time → D ∝ S. Percentage change shortcuts. Speed ↑20% → time ↓16.67% (×5/6, since ×6/5 on speed); the multiplier logic from Part 3 does the work.

What should you know about 4. Relative Speed: The Concept That Runs Trains, Boats and Escalators?

Same direction: relative speed = difference . Opposite directions: relative speed = sum . Everything in sections 4–6 is this one-line applied. Time = (length to be covered) —relative speed. The “length to be covered” is the sum of lengths when two trains pass each other. The train’s own length when passing a pole/man (a man’s length is zero — that’s the whole trick).

What should you know about 5. Trains: The Four Standard Wrappers?

Train past a pole/man: T = train length —speed. Train past a platform/bridge/tunnel: T = (train + platform length) —speed. Two trains crossing (opposite): T = (L₁+L₂) —(S₁+S₂). Two trains crossing (same-direction): T = (L₁+L₂) —(S₁−S₂). The faster must start behind — read who overtakes whom.

Related reading: CSAT Part 3: Percentages, Ratio and Speed Math

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