Let us study some basic time and work concepts. In our daily lives, we come across so much work that needs to be completed within a specific time period. Usually, some persons are specifically designated to do these works. What will we do, if after some time we realize that the above said work would not be completed in the desired time? We assign more guys to help the earlier people and finish the work in time. This makes the very basic concept of time and work i.e. more people finish the work in lesser time, and lesser persons take more time to finish work.
Let us assume a well has to be dug which has to be done in 10 days. If a person can dig a well in 10 days, then in 1 day he will dig 1/10th of that well. This basic approach can be applied to solve a majority of the time and work problems.
Combined formula for Time and Work
Another important concept that is used in time work problems is the combined efficiency of two or more persons. In questions on time and work, the rates at which certain persons or machines work alone are usually given, and it is necessary to compute the rate at which they work together (or vice versa).
Let us say, for example, it takes 3 & 6 hours for Bahubali and Kattappa, respectively, to break a dam working alone. So, in 1 hour Bahubali would have broken one-third or 1/3rd or 33% of the dam and Kattappa would have broken one-sixth or 1/6th or 16.67% of the dam. In 2 hours, Bahubali would have destroyed 1/3*2 or 33% *2 = 66.66% of the dam and kattappa would have destroyed 1/6th *2= 1/3= 33.33% of the dam. So if Both Bahubali and Kattappa work together, they would have destroyed 66.66+ 33.33 (2/3+1/3) or 100% of the dam in 2 hours. Therefore, if both worked together for 1 hour, they would have destroyed 1/3 + 1/6= ½ or half of the dam. Thus in 2 hours, the dam is destroyed.
Generalizing, we conclude that in 1 hour, Bahubali does 1/r of the job, Kattappa does 1/s of the job, and Bahubali & Kattappa together do 1/h of the job or that together they can finish the job in ‘h’ hours where the formula for work comes out as 1/r + 1/s = 1/h.
Time and Work Problems Tricks: LCM Approach
The same concept can be learned with unit’s work approach as well, which assumes the total work to be done as the LCM (Learn how to calculate LCM) of the number of days taken by each of the persons to complete the work. Let's assume that Trump can do a piece of work in 20 days working alone and Putin can do it in 30 days of his own. Now in the above-mentioned case, let us assume that the work consists of the LCM of 20 & 30 i.e. 60 units to be done by Trump & Putin. Since Trump completes 60 units in 20 days, so he completes 60/20 = 3 units of work per day. Similarly Putin completes 60 units of the work in 30 days, so he completes 60/30 = 2 units per day. They are doing the same work together, so they do 3 + 2 = 5 units per day. So, 60 units will be done in 60/5 = 12 days.
You should go through the following time and work examples in order to understand the concept better. This is one of the favorite areas of the examiner. You will see aptitude questions on time and work in almost all the competitive examinations. Go through the following illustrations to learn the concept of work and time and try to understand the time work questions.
Must Read Time and Work Problems Articles
Illustration 1: Samir can do a job in 30 days. In how many days can he complete 70% of the job?
Sol: Now as per the question he finishes the work in 30 days, or he can do 100% of the work in 30 days. If he has to do only 70% of the work, he will require 70% of the time.
Number of days required = 30 × 70/100 = 21 days.
Illustration 2: Reshma can do 75% job in 45 days. In how many days can she complete the job?
Sol: Every work is 100% in itself. Reshma does 75% of the work in 45 days. That means she does 1% of the work in 45/75 days and she will do 100% of the work in 100 × 45/75 = 60 days.
Illustration 3: John can do a piece of work in 60 days; he will do how much of the work in 40 days?
Sol: In 1 day, John does 1/60th of the work, so in 40 days he will do 40 × 1/60 = 2/3rd of the work.
Illustration 4: Anup can finish a piece of work in 30 days. He will finish what percent of the work in 15 days?
Sol: In 1 day, he does 1/30th of the work, and in 15 days, he will do 15/30th of the work which is 100 × 15/30 = 50%.
Illustration 5: Ria can do a piece of work in 40 days, she will take how many days to finish three-fourth of the work?
Sol: Ria can complete the work in 40 days. She will do ¾th of the work in ¾th of the total time. i.e. she will need 40 × 3/4 = 30 days.