**Time and Work Formulas:** Questions asked from Time and Work topic generally test mental ability of a student calculate the time in which a man/team complete the given work while efficiency of is given. While doing the questions of Time and Work, a most common approach that student must use is that-

**if a man completes 1 unit of work in N days, then amount/part of work done by him **** in 1 day is 1/n**

**Time and Work Concept**

Assume that work of man is to eat 100 chocolates and he eats all of them in 10 days, then amount of work done(chocolates eaten) in 1 day is (100/10)=10 chocolates eaten.

Or

If Rashmi can make 10 cakes in 5 hours, then amount of work done(Cake made) by her in 1 hour is (10/5)=2 cakes.

Another easy way to solve questions from this topic is % approach i.e ‘if a man can complete a work in 20 days, then amount of work done by him in 1 day is (100/20)%=5%.

**Time and Work Formulas**

Consider an example: Rahul can complete a work in 10 days and Arun can complete the same work in 20 days. Find the time in which the work will be completed if both of them work together.

There are three approaches to solve this:

**(i) TRADITIONAL APPROACH **

If Rahul can complete the work in 10 days, then amount of work done by him in 1 day =1/10 units.

Similarly amount of work done by Arun in 1 day = 1/20 units.

Hence when both of them work together, total work done is (1/10)+(1/20)=3/20 units.

Hence if 3/20 units of work is done in 1 day

**Then 1 unit of work will be completed in 20/3 days.**

**(ii) LCM APPROACH**

In this method, assume the LCM of days as a number of chocolates. LCM of 10 and 20 is 20. Now assume that there were 20 chocolates, and If Rahul take 10 days to eat them all, it can be concluded that he ate 2 chocolates per day. Similarly, Arun can eat 1 chocolate in a day.

Therefore,

They both will eat 3 chocolates in 1 day.

**Time taken to complete whole work (to eat all of them)= 20/3 days.**

**NOTE:** Our answer will be same, we consider any number of chocolates, but for easy calculation purpose we use a number that is easily divisible by number of days given.

**% APPROACH**

This method is kind of same as (i). Consider the work unit as 100% work.

Now note that if Rahul take 10 days to complete 100% of work, then work done by him in 1 day is 10%. Similarly work done by Arun in 1 day is 5%. Therefore, both of them working together will complete 15% of work in 1 day.

**100% of work will be completed in (100/15)=20/3 days.**

**In all these approaches, 1 common thing that occurs is to calculate amount/part/percentage of work done in 1 day.**

**LCM approach is best used in the questions in which efficiency of pipe or volume of tank is given.** Consider Example- Pipe A and Pipe B when both opened together can fill a tank in 4 minutes. Pipe A alone can fill it in 16 minutes. Find the time in which pipe B alone will fill the tank.

**In traditional way:**

Tank filled by Pipe A alone in 1 minutes = 1/16 units.

Let pipe B alone can fill it in x minutes.

Then tank filled by pipe B alone 1 minute is=1/x unit.

Therefore, (1/x)+(1/16)=(1/4)

(1/x)=(3/16), x=16/3

**LCM APPROACH:**

Let total units of tank are 16 liters. It means A can fill 1 liter in a minute. Assume that B fills x unit in minute. Tank was filled in 4 minutes’ means

4(x+1)=16

x+1=4

X=3 units per minute

time taken is 16/3 minutes.

**All this could be done was mentally through LCM method. Give it a try!**

**MAN-DAYS-HOUR-WORK THEOREM:**

According to this theorem if more than 1 man of equal efficiency are working together on a same work, then amount/part of work done by them is directly proportional to the time given to work by number of man. In more simple words work done depends on efficiency and total time given.

For eg. 10 men in 5 days can do same amount of work as 5 men in 10 days or if we explore it more we can see 10 men in 6 days working 4 hours a day can do same amount of work as 30 men in 4 days working 2 hours a day.

Please verify above two examples, by assuming a man can eat 1 chocolate in 1 hour and try to solve given problem.

**QUESTION**

Men working 4 hours a day can complete 48% of work in 8 days. Calculate how many men are required to complete 2 units of a work, if they have to complete it in 10 days, 8 hours a day.

**SOLUTION**

In this type of problems, by default we have to assume that all men have equal efficiency and they do the work with uniform speed.

**Applying Man-day-hour formulae**

**Another type of concept that is introduced here is when people with unequal efficiencies are working,** for eg. 4 women can do the same amount of work in a given time as 3 men. For these type of questions, we use ratio approach, we simply write

4W= 3M

=> W/M=3/4.

And then we consider efficiency of a men as 4 units and that of women as 3 units throughout the problem.

**Few points to always remember:**

- If the ratio of efficiencies of two persons is x:y then ratio of respective time taken by them is y:x.
- If X is N times efficient than Y, time taken by X to complete a work is 1/N time of time taken by Y.
- Total work done by a man of efficiency X in N days is NX units.

**Time and Work Questions**

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