Time and Work Questions for CDS

The Core Concept: Work as a Rate

Think of work as filling a bucket. If A can fill it in 5 days, each day A fills 1/5 of the bucket. This fraction is A's daily work rate. The golden rule: Work = Rate x Time. When workers work together, you simply add their individual rates. This single idea solves 80 percent of Time and Work problems.

• If a person completes a job in N days, their work rate per day = 1/N
• Two people working together: combined rate = 1/A + 1/B
• Time taken together = 1 divided by (combined rate) = AB/(A+B)
• Total work is always treated as 1 unit (or use LCM as total units)
• If a person leaves early, split the timeline and account for partial contributions separately

LCM Method: The Speed Shortcut

Instead of working with fractions, assign actual units to the total work equal to the LCM of all given days. Then find each person's daily output in units. This avoids fraction arithmetic and is faster under exam pressure. CDS aspirants who use the LCM method typically save 30-40 seconds per question.

• Step 1: Find LCM of all individual time values given in the problem
• Step 2: That LCM is your total work in units
• Step 3: Each person's daily work = LCM divided by their individual time
• Step 4: Add daily units for people working together, then divide total by combined daily units
• Works cleanly for pipe-and-cistern problems too — inflow adds, outflow subtracts

Pipes and Cisterns

This is the same concept in a different disguise. Pipes filling a tank = workers doing positive work. Pipes draining = workers doing negative work. A filling pipe that takes X hours has rate +1/X. A draining pipe that empties in Y hours has rate -1/Y. Combine rates and take reciprocal for net time. CDS frequently swaps between work problems and pipe problems — do not let the language change fool you.

• Inlet pipe rate is positive, outlet pipe rate is negative
• Net rate = sum of all inlet rates minus sum of all outlet rates
• If net rate is negative, tank is emptying not filling
• Time to fill = 1 / net rate (only if net rate is positive)
• Classic CDS twist: tank is half full when both pipes open — adjust remaining work accordingly

Work Done in Parts: Workers Joining or Leaving

A very common CDS pattern: A works for some days, then B joins, or A leaves before the job ends. Handle these by calculating work done in each phase separately. Use remaining work after each phase to find time for the next phase. The LCM method makes phase calculations very clean since you work with whole numbers.

• Phase 1: only some workers present — calculate units done
• Phase 2: different set of workers — calculate remaining units and time
• Always verify: total work done across all phases = LCM (or 1 if using fraction method)
• Alternate days pattern: A works odd days, B works even days — find work per 2-day cycle then scale up
• If asked when work gets exactly completed, check if it falls mid-cycle on alternate day problems

• Using T = AB/(A+B) when more than two workers are involved — this formula is ONLY for two people; for three or more, always add rates first then take reciprocal
• Forgetting to subtract outlet rates in pipe problems — many aspirants add all pipe times and get a wrong combined time
• Confusing efficiency with time — if A is twice as efficient as B, A takes HALF the time, not double; the ratio is inverse
• In alternate days problems, checking only complete cycles and missing a partial day at the end — always check if remaining work after full cycles gets done on the next half-cycle
• Taking LCM of combined time instead of individual times — always find LCM of the individual worker times, not the together time

• RATE + RATE = TOGETHER RATE: think of two taps filling one tub — water flow adds up, not time
• Mnemonic for Pipes: FILL is Plus, DRAIN is Minus — F for Fill = Forward = Plus sign
• LCM trick memory hook: LCM is the Total Pizza — each worker eats slices per day, divide pizza by slices-per-day to get days
• For the two-worker formula AB/(A+B), remember it as Product over Sum — POS: P=Product on top, S=Sum below

• CDS typically places 2-3 Time and Work questions in each Maths paper; at least one will be a pipe-and-cistern variant, so do not skip that section
• Expected difficulty is medium — questions are solvable in 90 seconds with LCM method; if you are spending over 2 minutes, skip and return
• A common CDS pattern is: give time for A alone and time for A+B together, then ask for B alone — practice 1/B = 1/together - 1/A reflexively
• Recent CDS papers have included a worker efficiency twist: A is 50 percent more efficient than B — translate this to time ratio immediately (A:B time = 2:3) before solving
• Do not solve with decimals mid-calculation; keep fractions or use LCM integers to avoid rounding errors that cost marks in MCQ format