Aptitude - Time and Work - Discussion

Please, Explain this with LCM method.

E * t = w.

Since e is inverse of t so 20 becomes 1/20.
Now 1/20*t=1/3 since we have to find the time taken so,
T =20/1/3 HENCE T= 60 because in LHS it is multiplication so after coming to RHS it will divide.

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.

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=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.

Why the reaming work is -1? Explain it please.

Still, I can't understand this. Can anyone help me to get it?

@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.

I'm not getting it, please help me by explaining in detail.

A+B' s can finish work = 30 days
if,
A+B work together = 20 days
Therefore, 30:20 =3:2 (3 is the total work & 2 is together work)
= 3-2 = 1 (1 is remaining A's work)

A's remaining work is 20 days
= 20 * 3 = 60 days.