Time and Work problems are undoubtedly one of the most important set of questions when you are preparing for competitive exams like IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, SSC CGL, SSC CHSL etc. Read on to boost your basics along with a list of time and work formulas.
If you want to crack exams like IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, SSC CGL, SSC CHSL and other competitive exams, you can’t dodge time and work problems for really long. Though this topic can be slightly tricky, however if your basics are strong and you know how the time and work formulas were derived and which time and work formulas to use in specific kinds of problems you are sorted! However, if none of the above is true for you, don’t worry, because we are going to discuss the fundamental concepts of this topic in this blog along the principles that help reach time and work formulas.
What is Time and Work?
Time and Work involves dealing with the rate at which individuals or group of people work. Conventionally we start by assuming the number of days (T) taken by a single person to complete a certain task where the rate of work of the person, or the amount of work the person can do in one day, is represented as 1/Tth part of the work.
Rate of work is the most important concept in Time and Work problems because it makes it possible, to sum up the effort of different people working together where each of them has a different rate of work over a unit of time.
Important Terms for Time and Work Formulas-
Before we plunge into time and work formulas, let’s quickly go through the different terms that make up time and work formulas-
Work (W) – The total amount effort or labour required to complete a given task is called work. It is represented by the letter ‘W’ and is always considered as a whole or one in every problem.
Person/ People (P) – The number of individuals involved in completing the given work is called people/person. It is represented by the letter ‘P’.
Time (T) – The exact count taken by the clock to complete a certain task is called time. It is represented by the letter ‘T’. Time can be calculated in two ways- the number or days ‘D’ or the number of hours ‘H’.
Rate of Work (R) – The amount of work done in a unit of time is called the rate of work. It can be calculated on a daily or hourly basis, depending on the conditions given in the questions. It is represented by the letter ‘R’.
Relationship b/w Terms for Time and Work Formulas
Now that we know the terms used in time and work formulas, let’s establish the relationship between then, this will help you to tweak time and work formulas as per the need of the questions.
We know for the definitions of terms that ‘Work Done’ is always proportional to the ‘Number of People’ doing the work, if the ‘Time’ is constant-
This implies that if we need to do more work we need more people and if we need to do less work we need less people.
We also know that ‘Work Done’ is always proportional to the ‘Time taken to do the Work’, if the ‘Number of People’ is constant.
Therefore to complete more work more time is needed and to complete less work less time is needed. Hence we can also say the same thing for the ‘Number of Hours’, hence-
In this case, the number of people and the number of days all of them worked for is constant.
Similarly, we can also say that-
From the above proportionality equations, we can say-
So, any change in any of these three parameters will affect Work Done.
If in a given set of time and work problems only hours or days is mentioned, you should eliminate the other variables.
List of Time and Work Formulas
1. If A can do a piece of work in n days,
2. If A does 1/n work in a day,
3. If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do W2 work in D2 days working H2 hours per day (where all men work at the same rate of work),
4. If A can do a piece of work in p days and B can do the same in q days,
Time and Work Problems based on Time and Work Formulas
Problems discussed in this section are based on time and work formulas we have discussed above.
Problem 1: 15 men can type 3240 pages in 6 days, working 2 hours per day. How many men would be required to type 5400 pages, working 4 hours for 3 days?
This problem can be solved by choosing the appropriate formula from the list of time and work formulas.
Let us assume the number of men needed to be ‘M’. Based on the data give, the work here is nothing but the number of pages to be typed. Substituting the values in the formula we get-
3240 / 5400 = (15 x 6 x 2) / (M x 3 x 4)
M = 25
Therefore, 25 men will be needed to complete the work in 3 days.
Problem 2: 4 men work 12 hours daily, to complete a work in 9 days. If 6 men work 2 hours daily, in how many days will the work be completed?
Unlike the previous problem, the work done here is not specified, so we will assume the ‘Work Done’ to be 1 and then proceed ahead by substituting the values in the formula.
So, substituting values we get-
4 x 9 x 12 = 16 x D x 2
D = 27/ 2 = 13.5 days
Therefore 6 men will take 13.5 days to complete the work.
Practice Problems based on Time and Work Formulas
Question 1: 15 men can type 3240 pages in 6 days working 2 hours per day. How many men would be required to type 5400 pages working 4 hours per day for 3 days?
1) 10 2) 16 3) 12 4) 25 5) None of these
Question 2: If 5 workers collect 60 kg wheat in 3 days, how many kilogram of wheat will 8 workers collect in 5 days?
1) 80 kg 2) 100 kg 3) 120 kg 4) 160 kg 5) None of these
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