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# Note for Time and Work - TW by Placement Factory

• Time and Work - TW
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• Quantitative Aptitude
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Quantitative Aptitude Made Easy Page 1

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Quantitative Aptitude Made Easy Index Foreword ................................................................................... 1 Preface ....................................................................................... 3 Introduction ............................................................................... 5 Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Number System Average LCM & HCF Ratio & Proportion Percentage Partnership Mixtures & Alligations Simple Interest & Compound Interest Problems Based on Ages Profit & Loss Sequence & Series Time & Work Pipes & Cisterns Time & Distance Boats & Streams Calendar Clocks Permutation & Combination Probability Trigonometry Geometry Mensuration Data Sufficiency Data Interpretation Page 2

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Quantitative Aptitude Made Easy Chapter - 12 Time and Work Three main factors of Time and Work There is a definite relationship between Time and Work. In this concept, there are only three factors:  Time taken to complete a certain job  Unit of work done  Number of persons doing the job There is a mental relationship between these three, discussed as follows: Work done (W) = Number of days (Time taken) (T or D) × Number of men (M) W=D×M Some basic points More number of men can do more work i.e. both are directly proportional More number of men take less time to complete certain job i.e. both are inversely proportional By summarizing, we get = × Let us start solving some examples: Example 1: 10 men can cut 8 trees in 16 days. In how many days can 6 men cut 10 trees? Solution: This is a very simple example. You are given: W1 = 8 W2 = 10 M1 = 10 M2 = 6 D1 = 16 D2 = ? Using formula, = × = × ⇒D2 = 33.3 Concept of efficiency This means, "How much work one person can do in one day (expressed in percentage)" For example: A person can do a job in 2 days ⇒ He can do 50% work in one day Therefore, his efficiency will be 50% Just a 2-step concept This concept involves two steps to calculate efficiency:   Convert into fraction i.e. per day work Multiply with 100 i.e. convert into percentage Page 3

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Quantitative Aptitude Made Easy Try the following example first, then re-read above points Example 2: If a person can complete his work in 5days. What will be his efficiency? Solution: Number of days a person take to complete his work = 5 ⇒ He is doing 1/5 th work per day (converted into fraction) Convert it into percentage: 100/5 = 20% Therefore, his efficiency is 20%. Summarizing, If a person can do his job in n days, efficiency will be Efficiency = % Note: Negative efficiency cancels the positive efficiency For Example: Positive efficiency = 5% Negative efficiency = 1.5% Net efficiency = 5- 1.5 = 3.5% As we all know, in competitive exams time management is very important. I suggest you to learn the fractions till 15. Number of days required to complete work N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Work/Day Efficiency (%) 1/n 1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12 1/13 1/14 1/15 100/n 100 50 33.33 25 20 16.66 14.28 12.5 11.11 10 9.09 8.25 7.69 7.14 6.66 Example 3: A can do a job in 10 days. B can do a job in 5 days. In how many days they can complete the job if they work together? Solution: Consider the above table A's efficiency = 10% B's efficiency = 20% A+ B efficiency = 10 + 20 = 30% This means, In one day A and B together can do 30% of work. Therefore, Number of days A and B together take to do 100% of work = ⇒3.33 days Page 4