Infographic: Time & Work | Quantitative Aptitude (Quant) - CAT PDF Download

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Infographic: Time and Work
Core Principle
Time and Work problems revolve around 
efficiency, time taken, and total work 
completed. The key is understanding that 
efficiency is inversely proportional to time 
when work remains constant.
Two Problem Types
Finding time required to complete assigned 
work, or finding work completed in a given 
time period. Both use the same fundamental 
relationships.
Fundamental Concepts
1
Work as Unit
Total work is assumed as 1 unit (or 100%). 
This standardisation allows easy calculation 
of daily capacity and combined efficiency.
2
Capacity Formula
If A completes work in 'n' days, then A's one 
day work = 1/n. This fraction represents A's 
capacity or efficiency per day.
3
Combined Work
When A and B work together: Combined 
work per day = 1/a + 1/b = (a+b)/ab. Time to 
complete = ab/(a+b) days.
4
Inverse Relationship
More workers mean fewer days needed. 
More days mean more work completed. 
Efficiency ? 1/Time when total work is 
constant.
Three Solution Approaches
Unitary Method
When to use: Simple 
problems with small numbers
Drawback: Less efficient for 
large numbers or complex 
scenarios
Approach: Calculate one unit, 
then scale up
Percentage Method
When to use: When fractional 
calculations feel cumbersome
Process: Take total work as 
100%. If A does work in 'a' 
days, daily work = 100/a%
Benefit: Easier mental 
calculations
LCM Method 
Why best: Eliminates fractions 
entirely, works with whole 
numbers
Process: Take LCM of time 
periods as total work, calculate 
per-day efficiency
Speed: Fastest for competitive 
exams
Negative Work Concept
When one entity builds whilst another destroys, the destroyer performs negative work. This 
concept is crucial for pipes and cisterns problems.
Formula: If X makes in 'a' days and Y breaks in 'b' days, work per day = 1/a - 1/b = (b-a)/ab
Work Equivalence Method
This powerful technique uses the principle: Work Rate × Time = Work Done
Pipes and Cisterns
Pipes and cisterns are direct applications of Time and Work principles. Inlet pipes do positive work 
(filling), outlet pipes do negative work (emptying).
Basic Principle
Treat inlet efficiency as positive, outlet 
efficiency as negative. Calculate net 
efficiency per unit time, then find total time 
needed.
Solution Approach
Use LCM of all pipe times as cistern 
capacity. Calculate per-minute fill/empty 
rates. Net rate = (Sum of inlet rates) - (Sum 
of outlet rates).
Master Formula 
The universal formula that covers most time-and-work variations:
 =
W 
1
M × D × T × E 
1 1 1 1
 
W 
2
M × D × T × E 
2 2 2 2
Where: M = Men/Workers, D = Days, T = Hours per day, E = Efficiency, W = Work done
Men (M)
Number of workers 
available. More men 
complete work faster 
(inverse proportion when 
work is constant).
Days (D)
Number of days worked. 
More days means more 
work completed (direct 
proportion).
Hours per Day (T)
Daily working hours. 
More hours per day 
increases total work 
(direct proportion).
Efficiency (E)
Skill level or speed. 
Higher efficiency 
completes more work in 
same time (direct 
proportion).
Work (W)
Total work to be 
completed. Can be 
expressed as fraction of 
total or as actual units.
Formula Quick Reference
Two Workers Together
A completes in 'x' days, B in 'y' days. 
Together: xy/(x+y) days
Three Workers Together
A in 'x' days, B in 'y' days, C in 'z' days. 
Together: xyz/(xy+yz+zx) days
Finding Individual Time
A+B together in 'x' days, A alone in 'y' 
days. B alone: xy/(y-x) days
Efficiency vs Time
Efficiency × Time = Constant (when work is 
same). E¡D¡ = E¢D¢