**Example: So if I say that a person can complete a work in 15 days that means he will do 1/15 work in one day, It’s simple maths.**

**Now another person does the same work in 30 days. So he will do 1/30 work in 1 day.**

**Now if i ask in how many days they will complete the work together. What we gonna do is Add their 1 day of work**

** like 1/15 + 1/30 = (2+1)/30 = 3/30 = 1/10 **

**Now this 1/10 we got is actually their 1 day work, So if they do 1/10 work in one day then it’s simple they will complete the whole work in 10 days.**

Now that was the conventional method and I believe that you all know how to solve Questions through Conventional method.

**So now lets move on to the Faster method i.e efficiency method.**

In efficiency method the Work is not treated in numerical value, Like in Conventional method the work is 1 but here the work is treated as percentage.

**So by common sense the work is always treated as 100%**

So when i say a person completes a work in 15 days it means he will do 100/15 % work in 1 day i.e 6.66% work in 1 day

If another person does the work in 30 days that means he will do 3.33% work in 1 day.

And together they will do 6.66 + 3.33 = 9.99 or 10% work in one day So in how many days they will do the complete work, that will be 100/10 = 10 days.

Now it may sound difficult That we have to convert Each value in % but don’t worry you don’t have to convert each value, You just have to learn all the values till 1/30 and then it will be a cakewalk.

Now we will take Some standard Cases Of time and work and you all are free to ask any problem if you have in any case.

### Case 1** – A does a work in X days, B does a Work in Y days In how many days they will complete the work.**

**Question- A completes the work in 10 days and B completes the work in 15 days In how many days they will complete the work.**

**Conventional Method **

Work done by A in 1 day = 1/10

Work Done by B in 1 day = 1/15

Work done By A & B together in 1 day = 1/10 + 1/15 = (3+2)/30 = 5/30 = 1/6

As A & B Completes 1/6 work in one day So they will complete the whole work in 6 Days.

**Efficiency method.**

Efficiency of A =100/10 = 10%

Efficiency of B = 100/15 = 6.66%

Efficiency of A & B Together = 10+ 6.66 = 16.66%

So the time taken by A & B together to Complete the work will be 100/16.66 = 6 Days.

**Case -2 A can do a work in X days and B can do it Y days, In how many days the work is completed if they work alternatively Started by A.**

Now in these type of question the person are not actually working together, what happens in this type of question is that A works for 1 day and then on 2nd day B work and on 3rd again A work and on Fourth again B works and so on till the work is completed.

For example A can do a work in 10 days B can do it 15 days and how many days they will finish it if The work is started by A

So again work done by A in one day = 1/10

” ” ” ” ” B ” ” = 1/15

Now the work done by Togther will be = 1/10 + 1/15 = 1/6 [ Note now this 1/6 work is not done by them in 1 day but in 2 days Actually, See A worked for 1 day and did 1/10 work on the second day B worked and finished the 1/15 work So in total 2 days they did 1/6 work]

So in 2 days they did 1/6 work so in how many days they will complete the whole work, Simple 12 days.

**Efficienecy Method**

A’s Efficiency = 10%

B’s Efficiency = 6.66%

A + B Efficiency = 16.66%

Work done by A and B in 2 days [ remember 2 days because they are not working together but working alternatively] = 16.66%

So time taken by them to complete 100% work = 100/(16.66 = 6 [ but always remember multiply this by 2, Beacause 16.66% work is done by them in 2 days and not in 1 day.

So The answer will be 6*2 = 12 days.

**Case 3: A can do a work in X days, B can do the work Y days and A leaves after working Z days.**

**Question- A can do a work in 10 days and B can do it in 15 days, A works for 2 days and then leaves, In how many days will the work be completed?**

Now here we can se that A leaves after 2 days that means A and B only worked for 2 days and the remaining work is done by B alone.

So first we have to calculated the work done by A and B together in 2 days.

So work done be A in 1 day = 1/10

“” ” ” ” B ” ” ” = 1/15

Work done by A & B together is 1 day = 1/10 + 1/15 = 1/6

Work done by A & B together in 2 days = (1/6) * 2 = 1/3

So remaining work = 1 – 1/3 = 2/3

Now this 2/3 work has to be done by B alone.

So it takes 15 days for B to do Complete work, How much time it will be taken by B to do 2/3 work ? So it will be 15*(2/3) = 10 days

So the work will be completed in 2 + 10 days = 12 days

**Efficiency method **

A’s efficiency = 10%

B’s Efficiency = 6.66%

Total a+b = 16.66%

work done by A and B together in 2 days = 16.66*2 = 33.33%

Work remaining = 66.66%

time taken by B to complete 66.66% work = 66.66/6.666 = 10 days

Total time = 10+2 = 12 days

**Case 4**

**A can do a piece of Work in 10 days and B can do it in 15 days, In how many days will the work be completed if B leaves 2 days before the completion on work.**

Now in this question B leaves before 2 days

Together they can do the work in what = 1/10 + 1/15 = 1/6

That means 6 Days.

That means Together they could have completed the work in 6 days but B works only till 4th day and The remaining work will be done by A alone

So they worked together for 4 days in all So work done by them in 4 days = (1/6)*4 = 4/6 = 2/3

remaining work = 1/3

Now this 1/3 work will be done by A alone

Now A can do the complete work in 10 days, So the time taken by him to do 1/3 work = 10 * (1/3) = 10/3 days or 3.33 days

So total time taken = 4+ 3.33 days = 7.33 days

**Efficiency method**

A’s efficiency = 10%

B’s efficiency = 6.66%

Total = 16.66%

Work will be completed in 6 days

Work done in 4 days = 66.66%

remaining = 33.33%

A will complete the remaining in = 33.33/10 = 3.33

Total = 4+3.33 = 7.33

**Case 5: A can do a Work in X days B can Do it in Y days, In how many days The work will get completed if B leaves 2 days before the actual completion of work.**

**Question: A can do a work in 10 days B can do it in 15 days, In how many days The work will get completed if B leaves 2 days before the Actual Completion of Work.what is the difference between this Actual completion of work and Completion of Work?**

See in last example the work was supposed to get completed in 6 days, So we just Solved the question taking into consideration that B leaves 2 days before the completion of work i.e B worked for 4 days and the rest 2 days work was don by A alone and Completes that work in 3.33 days Total 7.33 days.

So if i ask In this question If B left 2 days before the actual completion then it means B should have left on 5.33 days Got it ?

Now back to the question.

Now just imagine that the work gets completed in x days.

So A would work for x days[ A works for the whole time ]

And B would work for x-2 days[ because B left 2 days before the actual completion of work]

So now According to Question

x/10 + (x-2)/15 = 1 [ Beacuse work is always one ]

(3x+2x-4)/30 = 1

5x -4 = 30

5x = 34

x = 6.8 days.

So the work will be completed in 6.8 Days.

It can also be asked That after how many days B left, So the answer would be Simple 6.8 – 2 = 4.8 days

**Efficiency Method**

A’s Efficiency = 10%

B’s Efficiency = 6.66%

Let the no. of days be x

so Accordring to question

10x + 6.66(x-2) = 100[ Work is always 100% in efficiency method ]

10x + 6.66x – 13.33 = 100

16.66x = 113.33

x = 113.33/16.66 = 6.8

Answer = 6.8 days