Time and Work

Time and Work

Core formulas:

Work = rate * time
If A finishes in x days, A's one-day work = 1/x
Together time for A and B = xy / (x + y)

LCM method:

1. Take total work as LCM of individual times.
2. Efficiency = total work / time.
3. Combined time = total work / combined efficiency.

Efficiency-time relation:

Efficiency ratio = inverse of time ratio
If A:B efficiency = x:y, time ratio = y:x

Pipes and cisterns:

Inlet = positive rate
Outlet = negative rate
Net rate = sum of rates
Time = tank capacity / net rate

Wages:

Wage share ratio = efficiency * time worked

Common traps:

• If people leave/join, split into phases.
• Work done and time taken are inverse only when total work is fixed.