Time & work is a very integral part of Arithmetic. In this topic, a student has to calculate time taken to complete the following task by a group of people. This topic holds great importance in the Quantitative Aptitude section of various entrance examinations like CAT, XAT, NMAT, CMAT, SNAP etc. Due to an increase in the number of Arithmetic questions in the CAT exam, the number of Time & Work questions has also increased. A total of 5-6 questions are set on Arithmetic. Out of these, questions on Time & Work range from 2 to 3. The questions are tricky and usually demands a good hold on concepts.
Following Time & work Questions have been asked recently in past CAT papers:
1. John takes twice as much time as Jack to finish a job. Jack and Jim together take one-thirds of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them working together. In how many days will Jim finish the job working alone? ____________ [CAT 2020]
John = x units/day
Jack = 2x units/day
Jim = x units/day (1/3rd of John does = 3x units, out of which jack does 2x)
Total = 4x units/day
John’s time taken = x(n+3) = 4x × n
Then n = 1 day for 4x units
For x units, Jim will take 4 days
2. Anil alone can do a job in 20 days while Sunil alone can do it in 40 days. Anil starts the job, and after 3 days, Sunil joins him. Again, after a few more days, Bimal joins them and they together finish the job. If Bimal has done 10% of the job, then in how many days was the job done? [CAT-2019]
3. John gets Rs 57 per hour of regular work and Rs 114 per hour of overtime work. He works altogether 172 hours and his income from overtime hours is 15% of his income from regular hours. Then, for how many hours did he work overtime? [CAT-2019]
let the number of overtime hours for john = x
So no regular hours = 172 –x
Income from overtime hours = (x)*114
Income from regular hours = (172-x)*57
Total income = 114x + (172 –x)*57 = 172*57 + 57x
As per question 15% of (172 – x) *57 = 114x
15/100 (172 +x)= 2x
15*172* – 15x = 200x
215x = 15*172
x = 12
4. At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency? [CAT 2019]
A. 18 B. 12 C. 36 D. 24
Let usual efficiency of A = 2a and that of B = b
So total work = 12*(2a+b) = 24a+12b————1)
In 2nd case when efficiency of A is halved and efficiency of B get tripled , new efficiency of A = 2a/2 = a
New efficiency of B = b*3 =3b
Total work = 9(a+3b) = 9a+27b ——————-2)
From eq 1) and 2)
24a+12b = 9a + 27b
15a = 15b
So total work = 24a+12b = 24a+12a = 36a
Time taken by A alone to complete the work = 36a/2a = 18 days
There are some set concepts or types on which questions are framed. A thorough understanding of each type of problem would help in tackling the exam. Time & Work questions in CAT, XAT, SNAP, NMAT, etc. are of the following types:
1. Simple formula-based
2. Time and Work problems based on Equation: Questions are based on forming equations based on given data and solving them
3. Time and work Efficiency Concept: In this type, the efficiency of a person in comparison to another person, will be given. For example, Ram is twice as efficient as Shyam, Shyam finishes the work in 16 days, in how many days will they together complete the task?
4. Efficiency percentage is given, calculate the time: In this type of question, mostly the time taken by one person is given and the efficiency of the second person is also given, you are supposed to find the time taken by them together
5. Calculate Time when workers join/ leave in between tasks: Questions based on calculating the time taken by workers to finish a specific job when new workers join, or some workers leave the task in between
6. Negative work concept
7. Pipes and Cistern based: Time and work CAT question based on this type are very common; inlet and outlet pipes are kept open in a tank, and the time required to fill the tank has to be calculated. These questions can be a little tricky.
Preparing any topic from the scratch requires patience, hard work, and above all commitment. To prepare for Time & Work, here are some Level-wise preparatory guidelines to follow:
Level – 1
1. Learn Speed calculation: For an effective and quick calculation, be thorough with tables till 20, memorize squares till 30, and cubes till 15
2. Fraction – Percentage relation: Ratios, Fractions, and Percentage interchange help in solving Time and work difficult problems in a very small amount of time. Keeping them on tip of your finger will help you save time during the exam. Memorize the fraction-percentage interrelation. For example, 1/2 is 50%, 1/3 is 33.33%, and so on
3. Note down all the time and work formula in this chapter and keep revising them
4. Practice Time and work basic questions on Efficiency based problems, Pipes and Cisterns, and Capital division based on work done from MBAP CAT E Book (Concept Theory). You can also listen to Live Lecture Recording (Basic) on basic concept and MBAP lecture Assignment.
5. Questions on Pipes and Cisterns are asked quite frequently in CAT and XAT, so the basic should be clear
Level – 2
1. Practice conceptual questions on time and work from MBAP CAT E Book (Practice Questions)
2. Move on to more complex problems, attempt beginner and intermediate level mock on conceptual problems based on time & work from MBAP CAT Advance E books.
• and keep a watch on time. These questions are easy but take a lot of time if not attempted properly.
3. Keep attempting mocks to check your performance
4. Topic-wise mocks, provided by MBAP, can be utilized to enhance your performance
Level – 3
1. For advanced level preparation, start practicing Time and work aptitude questions from Arun Sharma
2. Problem on time and work in Arun Sharma are categorized into Level of Difficulty (LOD), based upon your preparation level, start attempting 3 or 4 questions daily.