Time and Work problems are about how long it takes to complete a task. If A can do a job in 10 days, A does 1/10 of the job each day. If A and B work together, their combined daily work = 1/10 + 1/8 = 9/40. So they finish in 40/9 days.
Key Formulas
1 day's work
If A completes work in n days → A's 1 day work = 1/n
Most fundamental formula!
Combined work
(A+B)'s 1 day work = 1/A + 1/B
Add their efficiencies.
Time together
Time = AB/(A+B) when A takes 'A' days and B takes 'B' days
Quick formula for two people.
Work remaining
Remaining work = 1 - work done so far
Crucial for 'A leaves after X days' type questions.
⚡ Shortcut Tricks
#1
Work ∝ Time: W1/W2 = T1/T2. More work = more time (same workers).
#2
Work ∝ Resource: W1/W2 = R1/R2. More workers = more work (same time).
#3
Time ∝ 1/Resource: R1/R2 = T2/T1. More workers = less time (same work). Inverse!
#4
Combined formula: W1/W2 = (R1×T1) / (R2×T2). The master formula for all Time-Work problems.
#5
Two working together: Time = (A×B)/(A+B). Example: A in 40 days, B in 60 days → together = 2400/100 = 24 days.
#6
Three working together: Time = (A×B×C)/(AB+BC+CA). Example: A=40, B=50, C=60 → 16.21 days.
#7
Work done in x days = x/Total days. Remaining work = 1 - work done.
#8
Salary ratio = inverse of time ratio (efficiency ratio). A in 20 days, B in 40 days → SA:SB = 40:20 = 2:1.
#9
Hours per day formula: W1/W2 = (R1×T1×H1)/(R2×T2×H2) where H = hours per day.
#10
Wages shared in ratio of work done (per day efficiency). Efficiency = 1/days taken.