UPP,UPSI, SSC CGL, CHSL, MTS ,NTPC, GROUP D ll TIME AND WORK ll by Dinesh sir

Описание: The *Time and Work* chapter is one of the most important and frequently asked topics in quantitative aptitude, especially in competitive exams like **SSC, Banking, Railway, Defence, and State PCS exams**. This chapter deals with the relationship between the amount of work done, the time taken to complete the work, and the number of workers involved.

Understanding this chapter properly helps students solve questions quickly and logically, as most problems are based on formulas and simple concepts rather than lengthy calculations.

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1. Basic Concept of Time and Work

The fundamental concept of this chapter is based on three quantities:

*Work*
*Time*
*Efficiency*

The relationship between them is:

*Work = Time × Efficiency*

This means:

If efficiency increases, time decreases.
If time increases, efficiency decreases.
Work is directly proportional to time and efficiency.

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2. Important Terms

1. Efficiency

Efficiency means the amount of work done in one unit of time.

For example:
If a person completes a work in 10 days,
Then his one day’s work = 1/10

This fraction (1/10) represents efficiency.

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2. One Day’s Work Formula

If a person can complete a work in **N days**, then:

One day’s work = 1/N

If two persons A and B take X and Y days respectively:

A’s one day work = 1/X
B’s one day work = 1/Y

If they work together:

Total one day work = (1/X + 1/Y)

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3. Types of Questions in Time and Work

#1 Individual Work

Questions where one person completes work alone.

Example:
A completes a work in 20 days.
Find his one day’s work.

Solution:
1/20

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#2 Combined Work

When two or more persons work together.

Example:
A completes a work in 10 days.
B completes the same work in 15 days.
How long will they take together?

Solution:
A’s one day work = 1/10
B’s one day work = 1/15

Total work per day = (1/10 + 1/15)
LCM = 30
= (3 + 2)/30
= 5/30
= 1/6

So, together they complete the work in 6 days.

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#3 Work and Wages

When wages are divided according to work done.

Rule:

Wages are divided in the ratio of efficiency.

If A does double work of B,
Then A gets double wages.

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#4 Work and Pipes & Cisterns

This is an application of Time and Work.

Filling pipe = Positive work
Emptying pipe = Negative work

Example:
One pipe fills a tank in 10 hours.
Another empties it in 20 hours.

Net work per hour = 1/10 – 1/20
= (2 – 1)/20
= 1/20

So, tank fills in 20 hours.

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#5 Men, Women and Children Problems

In these questions, efficiencies are compared.

Example:
2 men = 3 women
Efficiency ratio = 2M = 3W

So, 1M = 3/2 W

Such comparisons help solve questions easily.

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#6 Alternating Work

When A works one day, B works next day.

In such cases:

Calculate 2-day work.
Then divide total work accordingly.

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4. Important Formulas

1. Basic Formula

Work = Time × Efficiency
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2. If A is ‘n’ times as efficient as B:

Then:

A takes 1/n time of B
Time ratio = inverse of efficiency ratio

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3. LCM Method (Most Important Trick)

Assume total work = LCM of given days.

Example:
A completes work in 12 days
B completes in 18 days

LCM (12,18) = 36

So:
A’s efficiency = 36/12 = 3
B’s efficiency = 36/18 = 2

Together = 5 units per day

Time = 36/5 days

This method avoids fractions and makes calculations easy.

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#Partial Work

If A leaves work after few days and B completes it:

Step 1: Find work done by A
Step 2: Subtract from total work
Step 3: Calculate remaining time by B

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#Negative Efficiency

In leak or damage cases:
Subtract the work.

6. Short Tricks

✔ Time and Efficiency are inversely proportional
✔ Always take LCM as total work
✔ Add efficiencies when working together
✔ Subtract efficiencies when one removes work
✔ Ratio of time = inverse ratio of efficiency

7. Common Mistakes

❌ Not taking LCM
❌ Adding time instead of efficiency
❌ Ignoring units (days/hours)
❌ Mistakes in fraction addition
8. Importance in Competitive Exams

Time and Work is frequently asked in:

SSC CGL
SSC CHSL
IBPS PO/Clerk
SBI PO
Railway Exams
State Police Exams

Usually 2–4 questions are asked directly or indirectly.

It also forms base for:

Pipes and Cistern
Partnership
Work and Wages
Data Interpretation
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Real Life Applications

Time and Work concept is used in:

Construction planning
Factory production rate
Employee task allocation
Project management
Water tank filling systems

Understanding this chapter helps in logical thinking and improves calculation speed.
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Final Hashtags:

#TimeAndWork #QuantitativeAptitude #MathsForCompetitiveExams #SSCPreparation #BankingExams #AptitudeMaths #PipesAndCistern #WorkAndWages #ProblemSolvingSkills #ExamPreparation #MathTricks #LCMMethod #EfficiencyConcept