Quantitative Aptitude · Time & Work
Time and work — the unit method
5 min read
One technique that handles most time-and-work questions, including pipes and cisterns.
Almost every time-and-work question yields to the same idea: convert days into work done per day, add the rates, then invert.
If A finishes a job in 10 days, A's rate is 1/10 of the job per day. If B takes 15 days, B's rate is 1/15. Working together their combined rate is 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 per day, so they finish in 6 days.
The LCM shortcut is faster under exam conditions. Take the LCM of the given days as the total work. For 10 and 15 days, LCM = 30 units. A does 30/10 = 3 units a day, B does 30/15 = 2 units a day, together 5 units a day, so 30/5 = 6 days. No fractions at all.
Pipes and cisterns is the same topic with different words. A filling pipe has a positive rate, a draining pipe a negative one. A tank filled by a pipe in 6 hours and emptied by another in 9 hours, both open, nets 1/6 − 1/9 = 3/18 − 2/18 = 1/18, so 18 hours to fill.
Efficiency questions: if A is twice as efficient as B, A takes half the time. Efficiency and time are inversely proportional — writing that relationship down before starting prevents the most common inversion error.