TIME AND WORK
CSAT
Time and Work is one of the most logical and concept-driven chapters in CSAT. This topic does not demand complex mathematics; instead, it tests an aspirant’s understanding of efficiency, work distribution, and proportional reasoning. Many CSAT questions are framed in simple language but require correct interpretation of how work and time are related.
BASIC CONCEPT OF WORK
Meaning of Work
• Any task or job completed by a person or group
• In mathematics, work is assumed to be uniform unless stated otherwise
Key Assumption in CSAT
• Work rate of a person remains constant
• All persons work with the same efficiency throughout the given time
RELATION BETWEEN WORK AND TIME
Fundamental Rule
• More workers → less time
• Fewer workers → more time
Basic Relation
• Work ∝ (Number of persons × Time)
This implies:
• If work is fixed, number of persons and time are inversely proportional
WORKING EFFICIENCY
Efficiency
• Ability of a person to do work in a given time
Concept
• If A is more efficient than B, A will take less time to do the same work
Efficiency Relation
• Efficiency ∝ 1 / Time
CSAT Tip
• Person taking less time is always more efficient
FRACTION METHOD
Concept
• Assume total work = 1 unit
Example
• If A can do a work in 10 days
• Work done by A in 1 day = 1/10
BASIC SINGLE PERSON WORK PROBLEMS
Example Concept
• If a person completes a work in x days
• Daily work = 1/x
• Work in y days = y/x
COMBINED WORK (TWO OR MORE PERSONS)
Concept
• Combined work = Sum of individual work rates
Example
• A does work in 10 days → 1/10 per day
• B does work in 20 days → 1/20 per day
• Together work per day = 1/10 + 1/20 = 3/20
Time to complete work
• Total work / Combined work per day
RATIO METHOD IN TIME AND WORK
Concept
• If A takes x days and B takes y days
• Efficiency ratio = y : x
CSAT Use
• Helpful in group work and distribution questions
WORK AND WAGES
Concept
• Wages are proportional to work done
Rule
• Wage ratio = Work ratio = Efficiency ratio
Used in
• Group payment problems
• Labour distribution questions
PIPE AND CISTERN TYPE QUESTIONS
Concept
• Filling pipe does positive work
• Emptying pipe does negative work
MEN–DAYS CONCEPT
Meaning
• Work measured as product of number of men and number of days
Formula
• Work = Men × Days
Application
• If men increase, days decrease proportionally
PRACTICE QUESTIONS
Question 1
A can complete a work in 12 days and B can complete the same work in 18 days. In how many days will they complete the work together?
Question 2
A group of 10 men can complete a work in 15 days. How many days will 15 men take to complete the same work, assuming same efficiency?
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Subject: CSAT
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