Aptitude - Time and Work - Discussion

@All.

Here is the solution.

Together A + B takes 30 days to finish the work. So let us assume the total work to be 300 units(it can be any multiple of 30 to make the calculation easy) .

Therefore per day work efficiency of A+B together = 300/30 (work done = per day efficiency*time , so efficiency = work done/time taken) .

Thus A + B one day efficiency= 10 units.

Now ATQ, B left after 20 days, which means A + B worked together for 20 days. Therefore work done by A + B together in 20 days = 20 *10 = 200 (work done = one day efficiency * no of days worked )

Now remaining work = 300 - 200 = 100 units (total work - work done by A + B together)

Now A takes 20 days to finish the remaining work. Thus day efficiency of A = 100/20 = 5 units per day. ( Again using work done / time taken = per day work efficiency. Unitary method)
Thus per day efficiency of A = 5 units per day.

Now time is taken by A to finish the whole work alone = 300/5 = 60 days.. (total work / per day efficiency) . Hence A takes 60 days to finish the whole work alone.

Also, the people who want to know how much time will B take to do the whole work alone, the answer is again 60 days. Why?

Because per day efficiency of A + B together was 10 units, also after calculating A's per day efficiency was found out to be 5 units, thus B's per day efficiency= 10 - 5 = 5 units per day.

So it's the same as A, therefore B will also take 60 days to finish the whole work alone.

Now total work=30 units.

A + B complete the 30 units of work in 30 days.

So, in one day they together complete 1 unit of work.

In 20 days, they complete 20 units of work.

Agree?

Now remaining work is 30 units-20 units=10 units is remaining which will be completed by A.

A takes 20 days to complete the remaining 10 units of work.
So he does 10/20= 1/2 unit of work in one day.
If A completes 1/2 unit of work in one day, then how many days he will take to complete the entire 30 units of work?

30/ (1/2) = 60 days.

a+b=30 days ==>1/30 amount of work in a single day.

a and b worked for 20 days, (1/30)*20 = 2/3.

after b left, a completed the remaining 1-(2/3)=>1/3 amount of work in 20 days.

------for 20 days-------
a will done 1/3==>0.33 amount of work.

------if its 40 days----
a will done 2/3==>0.66 amount of work.

------if its 60 days------
a will done 3/3==>1 amount of work.

So, the answer is, A will take 60 days to complete the total(ie:1) amount of work.

Hope this helps.

A and B can complete the work in 30 days.

So 2 (1 unit by A and another 1 unit by B) units is completed per day.

30 * 2=60 is the total units completed in 30 days.

A and B together worked for 20 days and completed 20 * 2 = 40 units of work.

20 units are the remaining work to be done by A, only as B has left the job, so A's capacity is 1 unit a day so A takes 20 days to complete the job.

A can do a job completely by itself in 60 days as we know that it's capacity is 1 unit a day.

(A + B) together they can complete work in 30 days.
So on each day they will do (1/30) of the total work.
So it is given that A and B together did for the first 20 days,
For 20 days they can do 20 times of (1/30) i.e. 20/30,

Remaining work is done by A which is 10/30 or 1/3 of total work for 20 days.
(1/3) * (total work) =20 days.
Multiplying 3 on both sides.

You will get,
Total work is done in 20 * 3 = 60 days.

Assume painting a room A + B can complete in 30 days.
But they work for only 20 days and b left till now they have painted most of the room.
The remaining days left they can do work together is 10 days.
But A worked for 20 days to complete that 10 days of work MEANS.
A had worked DOUBLE days as they can work together.
So, A can alone can complete the work is DOUBLE of together work that is 30 * 2 = 60.

Consider 100% of the work can be completed by both A & B in 30 days, so this implies.

In 1 day A & B can complete 3.33% of work.

So A & B worked for 20 days which means they both completed 3.33*20 = 66.66% of work.

And now A alone need to finish 33.33% of work. But A finished in 20 days, which means.

A's Productivity is 1.66% per 1 day.

So A alone can complete it in = 60 days.

In efficiency method;

A+B = 1/30.

(B only work for 20 days that mean A & B work together only 20 days. The remaining 20 days A alone do it).

Now,

A+B = 20 days
A (alone)= 20 days.

Total work:

20(A+B)+ 20(A) = 1, (1 IS TOTAL WORK )
20(1/30)+20A = 1,
(2/3)+20A = 1,
2+60A = 3,
60A = 3-2,
60A = 1.
A = 1/60.
i. e, A = 60days.

A & B together works for 30 days
so, (A & B)'s 1 day work= 1/30
A&B worked for 20 days together
it is said after working together for 20 days b left
so, (A&B)'s work for 20 days together = (1/30)x20=2/3
remaining work that is to be done =1-2/3=1/3
1/3 work is done in 20 days
1 work i.e; complete work would be done in 20/(1/3)=20x3=60 days

A and B together complete the work in 30 days.

So (A+B) 1 day work is (1/30).

B worked for 20 days & left, so A did the remaining 10 days effective work alone in another 20 days.

10 days remaining work ---> A took 20 days.

Therefore 30 days work(i.e 1 complete work) is done in----> (20/10)*30 = 60 days.