Eduqo
Quantitative Aptitude›Ch 3: Time, Work & Distance›Time and Work Masterclass
Master unit work, efficiency, and LCM method for competitive exams
Total Work is always equal to Efficiency multiplied by Time. By assuming Total Work as the LCM of given days, we can easily find individual efficiencies and solve questions quickly.
Memory Hooks
| Given | LCM Work | Efficiencies |
|---|---|---|
| A: 10d, B: 15d | 30 units | A=3, B=2 |
| A: 12d, B: 24d | 24 units | A=2, B=1 |
| A: 20d, B: 30d | 60 units | A=3, B=2 |
Total Work
(LCM total units)
LCM total units
Assume LCM of days as total work.
Efficiency
(Daily work rate)
Daily work rate
Divide total work by days.
Together
(Add efficiencies)
Add efficiencies
A+B work together with summed speed.
Alternate
(Turn by turn)
Turn by turn
Calculate work done in 2-day cycles.
Adding days directly when working togetherAdd efficiencies, then divide total work
Never add days directly; always add daily efficiencies.
Stopping alternate cycle calculation prematurelyCheck remaining work before next person's turn
Always verify if the last incomplete cycle needs a full turn.
Confusing efficiency ratio with time ratioEfficiency is inversely proportional to time
If time ratio is 2:3, efficiency ratio is 3:2.
Q1.A can finish a work in 12 days and B in 15 days. In how many days will they finish it together?
Q2.A and B can do a piece of work in 10 and 15 days respectively. Working alternately starting with A, in how many days will the work be finished?