Study Notes On Time & Work

                              Time and Work

What actually the Time and Work Topic is all about? In simple words It's how much time a person will take to Complete a Given Work. 

Note -: In conventional Method work is always treated as 1 

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 going to 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 let’s 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 together 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. 

Efficiency 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, Because 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, firstly 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 3.33days 

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 remaning 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. 

Now, 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 day, 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 day work was done 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

Note Prepared By- Katherine Pierce ma'am

Regards,

Classroom Team